CINXE.COM

<!DOCTYPE html>    <html class="no-js"> <head> <meta charset="utf-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"><script type="text/javascript">(window.NREUM||(NREUM={})).init={ajax:{deny_list:["bam.nr-data.net"]}};(window.NREUM||(NREUM={})).loader_config={licenseKey:"bae5605f02",applicationID:"273632920"};;/*! For license information please see nr-loader-rum-1.274.0.min.js.LICENSE.txt */ (()=>{var e,t,r={8122:(e,t,r)=>{"use strict";r.d(t,{a:()=>i});var n=r(944);function i(e,t){try{if(!e||"object"!=typeof e)return(0,n.R)(3);if(!t||"object"!=typeof t)return(0,n.R)(4);const r=Object.create(Object.getPrototypeOf(t),Object.getOwnPropertyDescriptors(t)),o=0===Object.keys(r).length?e:r;for(let a in o)if(void 0!==e[a])try{if(null===e[a]){r[a]=null;continue}Array.isArray(e[a])&&Array.isArray(t[a])?r[a]=Array.from(new Set([...e[a],...t[a]])):"object"==typeof e[a]&&"object"==typeof t[a]?r[a]=i(e[a],t[a]):r[a]=e[a]}catch(e){(0,n.R)(1,e)}return r}catch(e){(0,n.R)(2,e)}}},2555:(e,t,r)=>{"use strict";r.d(t,{Vp:()=>c,fn:()=>s,x1:()=>u});var n=r(384),i=r(8122);const o={beacon:n.NT.beacon,errorBeacon:n.NT.errorBeacon,licenseKey:void 0,applicationID:void 0,sa:void 0,queueTime:void 0,applicationTime:void 0,ttGuid:void 0,user:void 0,account:void 0,product:void 0,extra:void 0,jsAttributes:{},userAttributes:void 0,atts:void 0,transactionName:void 0,tNamePlain:void 0},a={};function s(e){try{const t=c(e);return!!t.licenseKey&&!!t.errorBeacon&&!!t.applicationID}catch(e){return!1}}function c(e){if(!e)throw new Error("All info objects require an agent identifier!");if(!a[e])throw new Error("Info for ".concat(e," was never set"));return a[e]}function u(e,t){if(!e)throw new Error("All info objects require an agent identifier!");a[e]=(0,i.a)(t,o);const r=(0,n.nY)(e);r&&(r.info=a[e])}},9417:(e,t,r)=>{"use strict";r.d(t,{D0:()=>g,gD:()=>h,xN:()=>p});var n=r(993);const i=e=>{if(!e||"string"!=typeof e)return!1;try{document.createDocumentFragment().querySelector(e)}catch{return!1}return!0};var o=r(2614),a=r(944),s=r(384),c=r(8122);const u="[data-nr-mask]",d=()=>{const e={mask_selector:"*",block_selector:"[data-nr-block]",mask_input_options:{color:!1,date:!1,"datetime-local":!1,email:!1,month:!1,number:!1,range:!1,search:!1,tel:!1,text:!1,time:!1,url:!1,week:!1,textarea:!1,select:!1,password:!0}};return{ajax:{deny_list:void 0,block_internal:!0,enabled:!0,harvestTimeSeconds:10,autoStart:!0},distributed_tracing:{enabled:void 0,exclude_newrelic_header:void 0,cors_use_newrelic_header:void 0,cors_use_tracecontext_headers:void 0,allowed_origins:void 0},feature_flags:[],generic_events:{enabled:!0,harvestTimeSeconds:30,autoStart:!0},harvest:{tooManyRequestsDelay:60},jserrors:{enabled:!0,harvestTimeSeconds:10,autoStart:!0},logging:{enabled:!0,harvestTimeSeconds:10,autoStart:!0,level:n.p_.INFO},metrics:{enabled:!0,autoStart:!0},obfuscate:void 0,page_action:{enabled:!0},page_view_event:{enabled:!0,autoStart:!0},page_view_timing:{enabled:!0,harvestTimeSeconds:30,autoStart:!0},performance:{capture_marks:!1,capture_measures:!1},privacy:{cookies_enabled:!0},proxy:{assets:void 0,beacon:void 0},session:{expiresMs:o.wk,inactiveMs:o.BB},session_replay:{autoStart:!0,enabled:!1,harvestTimeSeconds:60,preload:!1,sampling_rate:10,error_sampling_rate:100,collect_fonts:!1,inline_images:!1,fix_stylesheets:!0,mask_all_inputs:!0,get mask_text_selector(){return e.mask_selector},set mask_text_selector(t){i(t)?e.mask_selector="".concat(t,",").concat(u):""===t||null===t?e.mask_selector=u:(0,a.R)(5,t)},get block_class(){return"nr-block"},get ignore_class(){return"nr-ignore"},get mask_text_class(){return"nr-mask"},get block_selector(){return e.block_selector},set block_selector(t){i(t)?e.block_selector+=",".concat(t):""!==t&&(0,a.R)(6,t)},get mask_input_options(){return e.mask_input_options},set mask_input_options(t){t&&"object"==typeof t?e.mask_input_options={...t,password:!0}:(0,a.R)(7,t)}},session_trace:{enabled:!0,harvestTimeSeconds:10,autoStart:!0},soft_navigations:{enabled:!0,harvestTimeSeconds:10,autoStart:!0},spa:{enabled:!0,harvestTimeSeconds:10,autoStart:!0},ssl:void 0,user_actions:{enabled:!0}}},l={},f="All configuration objects require an agent identifier!";function g(e){if(!e)throw new Error(f);if(!l[e])throw new Error("Configuration for ".concat(e," was never set"));return l[e]}function p(e,t){if(!e)throw new Error(f);l[e]=(0,c.a)(t,d());const r=(0,s.nY)(e);r&&(r.init=l[e])}function h(e,t){if(!e)throw new Error(f);var r=g(e);if(r){for(var n=t.split("."),i=0;i<n.length-1;i++)if("object"!=typeof(r=r[n[i]]))return;r=r[n[n.length-1]]}return r}},3371:(e,t,r)=>{"use strict";r.d(t,{V:()=>f,f:()=>l});var n=r(8122),i=r(384),o=r(6154),a=r(9324);let s=0;const c={buildEnv:a.F3,distMethod:a.Xs,version:a.xv,originTime:o.WN},u={customTransaction:void 0,disabled:!1,isolatedBacklog:!1,loaderType:void 0,maxBytes:3e4,onerror:void 0,ptid:void 0,releaseIds:{},appMetadata:{},session:void 0,denyList:void 0,timeKeeper:void 0,obfuscator:void 0},d={};function l(e){if(!e)throw new Error("All runtime objects require an agent identifier!");if(!d[e])throw new Error("Runtime for ".concat(e," was never set"));return d[e]}function f(e,t){if(!e)throw new Error("All runtime objects require an agent identifier!");d[e]={...(0,n.a)(t,u),...c},Object.hasOwnProperty.call(d[e],"harvestCount")||Object.defineProperty(d[e],"harvestCount",{get:()=>++s});const r=(0,i.nY)(e);r&&(r.runtime=d[e])}},9324:(e,t,r)=>{"use strict";r.d(t,{F3:()=>i,Xs:()=>o,xv:()=>n});const n="1.274.0",i="PROD",o="CDN"},6154:(e,t,r)=>{"use strict";r.d(t,{OF:()=>c,RI:()=>i,WN:()=>d,bv:()=>o,gm:()=>a,mw:()=>s,sb:()=>u});var n=r(1863);const i="undefined"!=typeof window&&!!window.document,o="undefined"!=typeof WorkerGlobalScope&&("undefined"!=typeof self&&self instanceof WorkerGlobalScope&&self.navigator instanceof WorkerNavigator||"undefined"!=typeof globalThis&&globalThis instanceof WorkerGlobalScope&&globalThis.navigator instanceof WorkerNavigator),a=i?window:"undefined"!=typeof WorkerGlobalScope&&("undefined"!=typeof self&&self instanceof WorkerGlobalScope&&self||"undefined"!=typeof globalThis&&globalThis instanceof WorkerGlobalScope&&globalThis),s=Boolean("hidden"===a?.document?.visibilityState),c=/iPad|iPhone|iPod/.test(a.navigator?.userAgent),u=c&&"undefined"==typeof SharedWorker,d=((()=>{const e=a.navigator?.userAgent?.match(/Firefox[/\s](\d+\.\d+)/);Array.isArray(e)&&e.length>=2&&e[1]})(),Date.now()-(0,n.t)())},1687:(e,t,r)=>{"use strict";r.d(t,{Ak:()=>c,Ze:()=>l,x3:()=>u});var n=r(7836),i=r(3606),o=r(860),a=r(2646);const s={};function c(e,t){const r={staged:!1,priority:o.P3[t]||0};d(e),s[e].get(t)||s[e].set(t,r)}function u(e,t){e&&s[e]&&(s[e].get(t)&&s[e].delete(t),g(e,t,!1),s[e].size&&f(e))}function d(e){if(!e)throw new Error("agentIdentifier required");s[e]||(s[e]=new Map)}function l(e="",t="feature",r=!1){if(d(e),!e||!s[e].get(t)||r)return g(e,t);s[e].get(t).staged=!0,f(e)}function f(e){const t=Array.from(s[e]);t.every((([e,t])=>t.staged))&&(t.sort(((e,t)=>e[1].priority-t[1].priority)),t.forEach((([t])=>{s[e].delete(t),g(e,t)})))}function g(e,t,r=!0){const o=e?n.ee.get(e):n.ee,s=i.i.handlers;if(!o.aborted&&o.backlog&&s){if(r){const e=o.backlog[t],r=s[t];if(r){for(let t=0;e&&t<e.length;++t)p(e[t],r);Object.entries(r).forEach((([e,t])=>{Object.values(t||{}).forEach((t=>{t[0]?.on&&t[0]?.context()instanceof a.y&&t[0].on(e,t[1])}))}))}}o.isolatedBacklog||delete s[t],o.backlog[t]=null,o.emit("drain-"+t,[])}}function p(e,t){var r=e[1];Object.values(t[r]||{}).forEach((t=>{var r=e[0];if(t[0]===r){var n=t[1],i=e[3],o=e[2];n.apply(i,o)}}))}},7836:(e,t,r)=>{"use strict";r.d(t,{P:()=>c,ee:()=>u});var n=r(384),i=r(8990),o=r(3371),a=r(2646),s=r(5607);const c="nr@context:".concat(s.W),u=function e(t,r){var n={},s={},d={},l=!1;try{l=16===r.length&&(0,o.f)(r).isolatedBacklog}catch(e){}var f={on:p,addEventListener:p,removeEventListener:function(e,t){var r=n[e];if(!r)return;for(var i=0;i<r.length;i++)r[i]===t&&r.splice(i,1)},emit:function(e,r,n,i,o){!1!==o&&(o=!0);if(u.aborted&&!i)return;t&&o&&t.emit(e,r,n);for(var a=g(n),c=h(e),d=c.length,l=0;l<d;l++)c[l].apply(a,r);var p=m()[s[e]];p&&p.push([f,e,r,a]);return a},get:v,listeners:h,context:g,buffer:function(e,t){const r=m();if(t=t||"feature",f.aborted)return;Object.entries(e||{}).forEach((([e,n])=>{s[n]=t,t in r||(r[t]=[])}))},abort:function(){f._aborted=!0,Object.keys(f.backlog).forEach((e=>{delete f.backlog[e]}))},isBuffering:function(e){return!!m()[s[e]]},debugId:r,backlog:l?{}:t&&"object"==typeof t.backlog?t.backlog:{},isolatedBacklog:l};return Object.defineProperty(f,"aborted",{get:()=>{let e=f._aborted||!1;return e||(t&&(e=t.aborted),e)}}),f;function g(e){return e&&e instanceof a.y?e:e?(0,i.I)(e,c,(()=>new a.y(c))):new a.y(c)}function p(e,t){n[e]=h(e).concat(t)}function h(e){return n[e]||[]}function v(t){return d[t]=d[t]||e(f,t)}function m(){return f.backlog}}(void 0,"globalEE"),d=(0,n.Zm)();d.ee||(d.ee=u)},2646:(e,t,r)=>{"use strict";r.d(t,{y:()=>n});class n{constructor(e){this.contextId=e}}},9908:(e,t,r)=>{"use strict";r.d(t,{d:()=>n,p:()=>i});var n=r(7836).ee.get("handle");function i(e,t,r,i,o){o?(o.buffer([e],i),o.emit(e,t,r)):(n.buffer([e],i),n.emit(e,t,r))}},3606:(e,t,r)=>{"use strict";r.d(t,{i:()=>o});var n=r(9908);o.on=a;var i=o.handlers={};function o(e,t,r,o){a(o||n.d,i,e,t,r)}function a(e,t,r,i,o){o||(o="feature"),e||(e=n.d);var a=t[o]=t[o]||{};(a[r]=a[r]||[]).push([e,i])}},3878:(e,t,r)=>{"use strict";function n(e,t){return{capture:e,passive:!1,signal:t}}function i(e,t,r=!1,i){window.addEventListener(e,t,n(r,i))}function o(e,t,r=!1,i){document.addEventListener(e,t,n(r,i))}r.d(t,{DD:()=>o,jT:()=>n,sp:()=>i})},5607:(e,t,r)=>{"use strict";r.d(t,{W:()=>n});const n=(0,r(9566).bz)()},9566:(e,t,r)=>{"use strict";r.d(t,{LA:()=>s,bz:()=>a});var n=r(6154);const i="xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx";function o(e,t){return e?15&e[t]:16*Math.random()|0}function a(){const e=n.gm?.crypto||n.gm?.msCrypto;let t,r=0;return e&&e.getRandomValues&&(t=e.getRandomValues(new Uint8Array(30))),i.split("").map((e=>"x"===e?o(t,r++).toString(16):"y"===e?(3&o()|8).toString(16):e)).join("")}function s(e){const t=n.gm?.crypto||n.gm?.msCrypto;let r,i=0;t&&t.getRandomValues&&(r=t.getRandomValues(new Uint8Array(e)));const a=[];for(var s=0;s<e;s++)a.push(o(r,i++).toString(16));return a.join("")}},2614:(e,t,r)=>{"use strict";r.d(t,{BB:()=>a,H3:()=>n,g:()=>u,iL:()=>c,tS:()=>s,uh:()=>i,wk:()=>o});const n="NRBA",i="SESSION",o=144e5,a=18e5,s={STARTED:"session-started",PAUSE:"session-pause",RESET:"session-reset",RESUME:"session-resume",UPDATE:"session-update"},c={SAME_TAB:"same-tab",CROSS_TAB:"cross-tab"},u={OFF:0,FULL:1,ERROR:2}},1863:(e,t,r)=>{"use strict";function n(){return Math.floor(performance.now())}r.d(t,{t:()=>n})},944:(e,t,r)=>{"use strict";function n(e,t){"function"==typeof console.debug&&console.debug("New Relic Warning: https://github.com/newrelic/newrelic-browser-agent/blob/main/docs/warning-codes.md#".concat(e),t)}r.d(t,{R:()=>n})},5284:(e,t,r)=>{"use strict";r.d(t,{t:()=>c,B:()=>s});var n=r(7836),i=r(6154);const o="newrelic";const a=new Set,s={};function c(e,t){const r=n.ee.get(t);s[t]??={},e&&"object"==typeof e&&(a.has(t)||(r.emit("rumresp",[e]),s[t]=e,a.add(t),function(e={}){try{i.gm.dispatchEvent(new CustomEvent(o,{detail:e}))}catch(e){}}({loaded:!0})))}},8990:(e,t,r)=>{"use strict";r.d(t,{I:()=>i});var n=Object.prototype.hasOwnProperty;function i(e,t,r){if(n.call(e,t))return e[t];var i=r();if(Object.defineProperty&&Object.keys)try{return Object.defineProperty(e,t,{value:i,writable:!0,enumerable:!1}),i}catch(e){}return e[t]=i,i}},6389:(e,t,r)=>{"use strict";function n(e,t=500,r={}){const n=r?.leading||!1;let i;return(...r)=>{n&&void 0===i&&(e.apply(this,r),i=setTimeout((()=>{i=clearTimeout(i)}),t)),n||(clearTimeout(i),i=setTimeout((()=>{e.apply(this,r)}),t))}}function i(e){let t=!1;return(...r)=>{t||(t=!0,e.apply(this,r))}}r.d(t,{J:()=>i,s:()=>n})},5289:(e,t,r)=>{"use strict";r.d(t,{GG:()=>o,sB:()=>a});var n=r(3878);function i(){return"undefined"==typeof document||"complete"===document.readyState}function o(e,t){if(i())return e();(0,n.sp)("load",e,t)}function a(e){if(i())return e();(0,n.DD)("DOMContentLoaded",e)}},384:(e,t,r)=>{"use strict";r.d(t,{NT:()=>o,US:()=>d,Zm:()=>a,bQ:()=>c,dV:()=>s,nY:()=>u,pV:()=>l});var n=r(6154),i=r(1863);const o={beacon:"bam.nr-data.net",errorBeacon:"bam.nr-data.net"};function a(){return n.gm.NREUM||(n.gm.NREUM={}),void 0===n.gm.newrelic&&(n.gm.newrelic=n.gm.NREUM),n.gm.NREUM}function s(){let e=a();return e.o||(e.o={ST:n.gm.setTimeout,SI:n.gm.setImmediate,CT:n.gm.clearTimeout,XHR:n.gm.XMLHttpRequest,REQ:n.gm.Request,EV:n.gm.Event,PR:n.gm.Promise,MO:n.gm.MutationObserver,FETCH:n.gm.fetch,WS:n.gm.WebSocket}),e}function c(e,t){let r=a();r.initializedAgents??={},t.initializedAt={ms:(0,i.t)(),date:new Date},r.initializedAgents[e]=t}function u(e){let t=a();return t.initializedAgents?.[e]}function d(e,t){a()[e]=t}function l(){return function(){let e=a();const t=e.info||{};e.info={beacon:o.beacon,errorBeacon:o.errorBeacon,...t}}(),function(){let e=a();const t=e.init||{};e.init={...t}}(),s(),function(){let e=a();const t=e.loader_config||{};e.loader_config={...t}}(),a()}},2843:(e,t,r)=>{"use strict";r.d(t,{u:()=>i});var n=r(3878);function i(e,t=!1,r,i){(0,n.DD)("visibilitychange",(function(){if(t)return void("hidden"===document.visibilityState&&e());e(document.visibilityState)}),r,i)}},3434:(e,t,r)=>{"use strict";r.d(t,{YM:()=>c});var n=r(7836),i=r(5607);const o="nr@original:".concat(i.W);var a=Object.prototype.hasOwnProperty,s=!1;function c(e,t){return e||(e=n.ee),r.inPlace=function(e,t,n,i,o){n||(n="");const a="-"===n.charAt(0);for(let s=0;s<t.length;s++){const c=t[s],u=e[c];d(u)||(e[c]=r(u,a?c+n:n,i,c,o))}},r.flag=o,r;function r(t,r,n,s,c){return d(t)?t:(r||(r=""),nrWrapper[o]=t,function(e,t,r){if(Object.defineProperty&&Object.keys)try{return Object.keys(e).forEach((function(r){Object.defineProperty(t,r,{get:function(){return e[r]},set:function(t){return e[r]=t,t}})})),t}catch(e){u([e],r)}for(var n in e)a.call(e,n)&&(t[n]=e[n])}(t,nrWrapper,e),nrWrapper);function nrWrapper(){var o,a,d,l;try{a=this,o=[...arguments],d="function"==typeof n?n(o,a):n||{}}catch(t){u([t,"",[o,a,s],d],e)}i(r+"start",[o,a,s],d,c);try{return l=t.apply(a,o)}catch(e){throw i(r+"err",[o,a,e],d,c),e}finally{i(r+"end",[o,a,l],d,c)}}}function i(r,n,i,o){if(!s||t){var a=s;s=!0;try{e.emit(r,n,i,t,o)}catch(t){u([t,r,n,i],e)}s=a}}}function u(e,t){t||(t=n.ee);try{t.emit("internal-error",e)}catch(e){}}function d(e){return!(e&&"function"==typeof e&&e.apply&&!e[o])}},993:(e,t,r)=>{"use strict";r.d(t,{ET:()=>o,p_:()=>i});var n=r(860);const i={ERROR:"ERROR",WARN:"WARN",INFO:"INFO",DEBUG:"DEBUG",TRACE:"TRACE"},o="log";n.K7.logging},3969:(e,t,r)=>{"use strict";r.d(t,{TZ:()=>n,XG:()=>s,rs:()=>i,xV:()=>a,z_:()=>o});const n=r(860).K7.metrics,i="sm",o="cm",a="storeSupportabilityMetrics",s="storeEventMetrics"},6630:(e,t,r)=>{"use strict";r.d(t,{T:()=>n});const n=r(860).K7.pageViewEvent},782:(e,t,r)=>{"use strict";r.d(t,{T:()=>n});const n=r(860).K7.pageViewTiming},6344:(e,t,r)=>{"use strict";r.d(t,{G4:()=>i});var n=r(2614);r(860).K7.sessionReplay;const i={RECORD:"recordReplay",PAUSE:"pauseReplay",REPLAY_RUNNING:"replayRunning",ERROR_DURING_REPLAY:"errorDuringReplay"};n.g.ERROR,n.g.FULL,n.g.OFF},4234:(e,t,r)=>{"use strict";r.d(t,{W:()=>o});var n=r(7836),i=r(1687);class o{constructor(e,t){this.agentIdentifier=e,this.ee=n.ee.get(e),this.featureName=t,this.blocked=!1}deregisterDrain(){(0,i.x3)(this.agentIdentifier,this.featureName)}}},7603:(e,t,r)=>{"use strict";r.d(t,{j:()=>P});var n=r(860),i=r(2555),o=r(3371),a=r(9908),s=r(7836),c=r(1687),u=r(5289),d=r(6154),l=r(944),f=r(3969),g=r(384),p=r(6344);const h=["setErrorHandler","finished","addToTrace","addRelease","addPageAction","setCurrentRouteName","setPageViewName","setCustomAttribute","interaction","noticeError","setUserId","setApplicationVersion","start",p.G4.RECORD,p.G4.PAUSE,"log","wrapLogger"],v=["setErrorHandler","finished","addToTrace","addRelease"];var m=r(1863),b=r(2614),y=r(993);var w=r(2646),A=r(3434);function R(e,t,r,n){if("object"!=typeof t||!t||"string"!=typeof r||!r||"function"!=typeof t[r])return(0,l.R)(29);const i=function(e){return(e||s.ee).get("logger")}(e),o=(0,A.YM)(i),a=new w.y(s.P);return a.level=n.level,a.customAttributes=n.customAttributes,o.inPlace(t,[r],"wrap-logger-",a),i}function E(){const e=(0,g.pV)();h.forEach((t=>{e[t]=(...r)=>function(t,...r){let n=[];return Object.values(e.initializedAgents).forEach((e=>{e&&e.api?e.exposed&&e.api[t]&&n.push(e.api[t](...r)):(0,l.R)(38,t)})),n.length>1?n:n[0]}(t,...r)}))}const x={};function _(e,t,g=!1){t||(0,c.Ak)(e,"api");const h={};var w=s.ee.get(e),A=w.get("tracer");x[e]=b.g.OFF,w.on(p.G4.REPLAY_RUNNING,(t=>{x[e]=t}));var E="api-",_=E+"ixn-";function N(t,r,n,o){const a=(0,i.Vp)(e);return null===r?delete a.jsAttributes[t]:(0,i.x1)(e,{...a,jsAttributes:{...a.jsAttributes,[t]:r}}),j(E,n,!0,o||null===r?"session":void 0)(t,r)}function T(){}h.log=function(e,{customAttributes:t={},level:r=y.p_.INFO}={}){(0,a.p)(f.xV,["API/log/called"],void 0,n.K7.metrics,w),function(e,t,r={},i=y.p_.INFO){(0,a.p)(f.xV,["API/logging/".concat(i.toLowerCase(),"/called")],void 0,n.K7.metrics,e),(0,a.p)(y.ET,[(0,m.t)(),t,r,i],void 0,n.K7.logging,e)}(w,e,t,r)},h.wrapLogger=(e,t,{customAttributes:r={},level:i=y.p_.INFO}={})=>{(0,a.p)(f.xV,["API/wrapLogger/called"],void 0,n.K7.metrics,w),R(w,e,t,{customAttributes:r,level:i})},v.forEach((e=>{h[e]=j(E,e,!0,"api")})),h.addPageAction=j(E,"addPageAction",!0,n.K7.genericEvents),h.setPageViewName=function(t,r){if("string"==typeof t)return"/"!==t.charAt(0)&&(t="/"+t),(0,o.f)(e).customTransaction=(r||"http://custom.transaction")+t,j(E,"setPageViewName",!0)()},h.setCustomAttribute=function(e,t,r=!1){if("string"==typeof e){if(["string","number","boolean"].includes(typeof t)||null===t)return N(e,t,"setCustomAttribute",r);(0,l.R)(40,typeof t)}else(0,l.R)(39,typeof e)},h.setUserId=function(e){if("string"==typeof e||null===e)return N("enduser.id",e,"setUserId",!0);(0,l.R)(41,typeof e)},h.setApplicationVersion=function(e){if("string"==typeof e||null===e)return N("application.version",e,"setApplicationVersion",!1);(0,l.R)(42,typeof e)},h.start=()=>{try{(0,a.p)(f.xV,["API/start/called"],void 0,n.K7.metrics,w),w.emit("manual-start-all")}catch(e){(0,l.R)(23,e)}},h[p.G4.RECORD]=function(){(0,a.p)(f.xV,["API/recordReplay/called"],void 0,n.K7.metrics,w),(0,a.p)(p.G4.RECORD,[],void 0,n.K7.sessionReplay,w)},h[p.G4.PAUSE]=function(){(0,a.p)(f.xV,["API/pauseReplay/called"],void 0,n.K7.metrics,w),(0,a.p)(p.G4.PAUSE,[],void 0,n.K7.sessionReplay,w)},h.interaction=function(e){return(new T).get("object"==typeof e?e:{})};const S=T.prototype={createTracer:function(e,t){var r={},i=this,o="function"==typeof t;return(0,a.p)(f.xV,["API/createTracer/called"],void 0,n.K7.metrics,w),g||(0,a.p)(_+"tracer",[(0,m.t)(),e,r],i,n.K7.spa,w),function(){if(A.emit((o?"":"no-")+"fn-start",[(0,m.t)(),i,o],r),o)try{return t.apply(this,arguments)}catch(e){const t="string"==typeof e?new Error(e):e;throw A.emit("fn-err",[arguments,this,t],r),t}finally{A.emit("fn-end",[(0,m.t)()],r)}}}};function j(e,t,r,i){return function(){return(0,a.p)(f.xV,["API/"+t+"/called"],void 0,n.K7.metrics,w),i&&(0,a.p)(e+t,[(0,m.t)(),...arguments],r?null:this,i,w),r?void 0:this}}function k(){r.e(296).then(r.bind(r,8778)).then((({setAPI:t})=>{t(e),(0,c.Ze)(e,"api")})).catch((e=>{(0,l.R)(27,e),w.abort()}))}return["actionText","setName","setAttribute","save","ignore","onEnd","getContext","end","get"].forEach((e=>{S[e]=j(_,e,void 0,g?n.K7.softNav:n.K7.spa)})),h.setCurrentRouteName=g?j(_,"routeName",void 0,n.K7.softNav):j(E,"routeName",!0,n.K7.spa),h.noticeError=function(t,r){"string"==typeof t&&(t=new Error(t)),(0,a.p)(f.xV,["API/noticeError/called"],void 0,n.K7.metrics,w),(0,a.p)("err",[t,(0,m.t)(),!1,r,!!x[e]],void 0,n.K7.jserrors,w)},d.RI?(0,u.GG)((()=>k()),!0):k(),h}var N=r(9417),T=r(8122);const S={accountID:void 0,trustKey:void 0,agentID:void 0,licenseKey:void 0,applicationID:void 0,xpid:void 0},j={};var k=r(5284);const I=e=>{const t=e.startsWith("http");e+="/",r.p=t?e:"https://"+e};let O=!1;function P(e,t={},r,n){let{init:a,info:c,loader_config:u,runtime:l={},exposed:f=!0}=t;l.loaderType=r;const p=(0,g.pV)();c||(a=p.init,c=p.info,u=p.loader_config),(0,N.xN)(e.agentIdentifier,a||{}),function(e,t){if(!e)throw new Error("All loader-config objects require an agent identifier!");j[e]=(0,T.a)(t,S);const r=(0,g.nY)(e);r&&(r.loader_config=j[e])}(e.agentIdentifier,u||{}),c.jsAttributes??={},d.bv&&(c.jsAttributes.isWorker=!0),(0,i.x1)(e.agentIdentifier,c);const h=(0,N.D0)(e.agentIdentifier),v=[c.beacon,c.errorBeacon];O||(h.proxy.assets&&(I(h.proxy.assets),v.push(h.proxy.assets)),h.proxy.beacon&&v.push(h.proxy.beacon),E(),(0,g.US)("activatedFeatures",k.B),e.runSoftNavOverSpa&&=!0===h.soft_navigations.enabled&&h.feature_flags.includes("soft_nav")),l.denyList=[...h.ajax.deny_list||[],...h.ajax.block_internal?v:[]],l.ptid=e.agentIdentifier,(0,o.V)(e.agentIdentifier,l),e.ee=s.ee.get(e.agentIdentifier),void 0===e.api&&(e.api=_(e.agentIdentifier,n,e.runSoftNavOverSpa)),void 0===e.exposed&&(e.exposed=f),O=!0}},8374:(e,t,r)=>{r.nc=(()=>{try{return document?.currentScript?.nonce}catch(e){}return""})()},860:(e,t,r)=>{"use strict";r.d(t,{$J:()=>o,K7:()=>n,P3:()=>i});const n={ajax:"ajax",genericEvents:"generic_events",jserrors:"jserrors",logging:"logging",metrics:"metrics",pageAction:"page_action",pageViewEvent:"page_view_event",pageViewTiming:"page_view_timing",sessionReplay:"session_replay",sessionTrace:"session_trace",softNav:"soft_navigations",spa:"spa"},i={[n.pageViewEvent]:1,[n.pageViewTiming]:2,[n.metrics]:3,[n.jserrors]:4,[n.spa]:5,[n.ajax]:6,[n.sessionTrace]:7,[n.softNav]:8,[n.sessionReplay]:9,[n.logging]:10,[n.genericEvents]:11},o={[n.pageViewTiming]:"events",[n.ajax]:"events",[n.spa]:"events",[n.softNav]:"events",[n.metrics]:"jserrors",[n.jserrors]:"jserrors",[n.sessionTrace]:"browser/blobs",[n.sessionReplay]:"browser/blobs",[n.logging]:"browser/logs",[n.genericEvents]:"ins"}}},n={};function i(e){var t=n[e];if(void 0!==t)return t.exports;var o=n[e]={exports:{}};return r[e](o,o.exports,i),o.exports}i.m=r,i.d=(e,t)=>{for(var r in t)i.o(t,r)&&!i.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},i.f={},i.e=e=>Promise.all(Object.keys(i.f).reduce(((t,r)=>(i.f[r](e,t),t)),[])),i.u=e=>"nr-rum-1.274.0.min.js",i.o=(e,t)=>Object.prototype.hasOwnProperty.call(e,t),e={},t="NRBA-1.274.0.PROD:",i.l=(r,n,o,a)=>{if(e[r])e[r].push(n);else{var s,c;if(void 0!==o)for(var u=document.getElementsByTagName("script"),d=0;d<u.length;d++){var l=u[d];if(l.getAttribute("src")==r||l.getAttribute("data-webpack")==t+o){s=l;break}}if(!s){c=!0;var f={296:"sha512-gkYkZDAwQ9PwaDXs2YM+rNIdRej1Ac1mupWobRJ8eahQcXz6/sunGZCKklrzi5kWxhOGRZr2tn0rEKuLTXzfAA=="};(s=document.createElement("script")).charset="utf-8",s.timeout=120,i.nc&&s.setAttribute("nonce",i.nc),s.setAttribute("data-webpack",t+o),s.src=r,0!==s.src.indexOf(window.location.origin+"/")&&(s.crossOrigin="anonymous"),f[a]&&(s.integrity=f[a])}e[r]=[n];var g=(t,n)=>{s.onerror=s.onload=null,clearTimeout(p);var i=e[r];if(delete e[r],s.parentNode&&s.parentNode.removeChild(s),i&&i.forEach((e=>e(n))),t)return t(n)},p=setTimeout(g.bind(null,void 0,{type:"timeout",target:s}),12e4);s.onerror=g.bind(null,s.onerror),s.onload=g.bind(null,s.onload),c&&document.head.appendChild(s)}},i.r=e=>{"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(e,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(e,"__esModule",{value:!0})},i.p="https://js-agent.newrelic.com/",(()=>{var e={840:0,374:0};i.f.j=(t,r)=>{var n=i.o(e,t)?e[t]:void 0;if(0!==n)if(n)r.push(n[2]);else{var o=new Promise(((r,i)=>n=e[t]=[r,i]));r.push(n[2]=o);var a=i.p+i.u(t),s=new Error;i.l(a,(r=>{if(i.o(e,t)&&(0!==(n=e[t])&&(e[t]=void 0),n)){var o=r&&("load"===r.type?"missing":r.type),a=r&&r.target&&r.target.src;s.message="Loading chunk "+t+" failed.\n("+o+": "+a+")",s.name="ChunkLoadError",s.type=o,s.request=a,n[1](s)}}),"chunk-"+t,t)}};var t=(t,r)=>{var n,o,[a,s,c]=r,u=0;if(a.some((t=>0!==e[t]))){for(n in s)i.o(s,n)&&(i.m[n]=s[n]);if(c)c(i)}for(t&&t(r);u<a.length;u++)o=a[u],i.o(e,o)&&e[o]&&e[o][0](),e[o]=0},r=self["webpackChunk:NRBA-1.274.0.PROD"]=self["webpackChunk:NRBA-1.274.0.PROD"]||[];r.forEach(t.bind(null,0)),r.push=t.bind(null,r.push.bind(r))})(),(()=>{"use strict";i(8374);var e=i(944),t=i(6344),r=i(9566);class n{agentIdentifier;constructor(e=(0,r.LA)(16)){this.agentIdentifier=e}#e(t,...r){if("function"==typeof this.api?.[t])return this.api[t](...r);(0,e.R)(35,t)}addPageAction(e,t){return this.#e("addPageAction",e,t)}setPageViewName(e,t){return this.#e("setPageViewName",e,t)}setCustomAttribute(e,t,r){return this.#e("setCustomAttribute",e,t,r)}noticeError(e,t){return this.#e("noticeError",e,t)}setUserId(e){return this.#e("setUserId",e)}setApplicationVersion(e){return this.#e("setApplicationVersion",e)}setErrorHandler(e){return this.#e("setErrorHandler",e)}addRelease(e,t){return this.#e("addRelease",e,t)}log(e,t){return this.#e("log",e,t)}}class o extends n{#e(t,...r){if("function"==typeof this.api?.[t])return this.api[t](...r);(0,e.R)(35,t)}start(){return this.#e("start")}finished(e){return this.#e("finished",e)}recordReplay(){return this.#e(t.G4.RECORD)}pauseReplay(){return this.#e(t.G4.PAUSE)}addToTrace(e){return this.#e("addToTrace",e)}setCurrentRouteName(e){return this.#e("setCurrentRouteName",e)}interaction(){return this.#e("interaction")}wrapLogger(e,t,r){return this.#e("wrapLogger",e,t,r)}}var a=i(860),s=i(9417);const c=Object.values(a.K7);function u(e){const t={};return c.forEach((r=>{t[r]=function(e,t){return!0===(0,s.gD)(t,"".concat(e,".enabled"))}(r,e)})),t}var d=i(7603);var l=i(1687),f=i(4234),g=i(5289),p=i(6154),h=i(384);const v=e=>p.RI&&!0===(0,s.gD)(e,"privacy.cookies_enabled");function m(e){return!!(0,h.dV)().o.MO&&v(e)&&!0===(0,s.gD)(e,"session_trace.enabled")}var b=i(6389);class y extends f.W{constructor(e,t,r=!0){super(e.agentIdentifier,t),this.auto=r,this.abortHandler=void 0,this.featAggregate=void 0,this.onAggregateImported=void 0,!1===e.init[this.featureName].autoStart&&(this.auto=!1),this.auto?(0,l.Ak)(e.agentIdentifier,t):this.ee.on("manual-start-all",(0,b.J)((()=>{(0,l.Ak)(e.agentIdentifier,this.featureName),this.auto=!0,this.importAggregator(e)})))}importAggregator(t,r={}){if(this.featAggregate||!this.auto)return;let n;this.onAggregateImported=new Promise((e=>{n=e}));const o=async()=>{let o;try{if(v(this.agentIdentifier)){const{setupAgentSession:e}=await i.e(296).then(i.bind(i,3861));o=e(t)}}catch(t){(0,e.R)(20,t),this.ee.emit("internal-error",[t]),this.featureName===a.K7.sessionReplay&&this.abortHandler?.()}try{if(t.sharedAggregator)await t.sharedAggregator;else{t.sharedAggregator=i.e(296).then(i.bind(i,9337));const{EventAggregator:e}=await t.sharedAggregator;t.sharedAggregator=new e}if(!this.#t(this.featureName,o))return(0,l.Ze)(this.agentIdentifier,this.featureName),void n(!1);const{lazyFeatureLoader:e}=await i.e(296).then(i.bind(i,6103)),{Aggregate:a}=await e(this.featureName,"aggregate");this.featAggregate=new a(t,r),n(!0)}catch(t){(0,e.R)(34,t),this.abortHandler?.(),(0,l.Ze)(this.agentIdentifier,this.featureName,!0),n(!1),this.ee&&this.ee.abort()}};p.RI?(0,g.GG)((()=>o()),!0):o()}#t(e,t){switch(e){case a.K7.sessionReplay:return m(this.agentIdentifier)&&!!t;case a.K7.sessionTrace:return!!t;default:return!0}}}var w=i(6630);class A extends y{static featureName=w.T;constructor(e,t=!0){super(e,w.T,t),this.importAggregator(e)}}var R=i(9908),E=i(2843),x=i(3878),_=i(782),N=i(1863);class T extends y{static featureName=_.T;constructor(e,t=!0){super(e,_.T,t),p.RI&&((0,E.u)((()=>(0,R.p)("docHidden",[(0,N.t)()],void 0,_.T,this.ee)),!0),(0,x.sp)("pagehide",(()=>(0,R.p)("winPagehide",[(0,N.t)()],void 0,_.T,this.ee))),this.importAggregator(e))}}var S=i(3969);class j extends y{static featureName=S.TZ;constructor(e,t=!0){super(e,S.TZ,t),this.importAggregator(e)}}new class extends o{constructor(t,r){super(r),p.gm?(this.features={},(0,h.bQ)(this.agentIdentifier,this),this.desiredFeatures=new Set(t.features||[]),this.desiredFeatures.add(A),this.runSoftNavOverSpa=[...this.desiredFeatures].some((e=>e.featureName===a.K7.softNav)),(0,d.j)(this,t,t.loaderType||"agent"),this.run()):(0,e.R)(21)}get config(){return{info:this.info,init:this.init,loader_config:this.loader_config,runtime:this.runtime}}run(){try{const t=u(this.agentIdentifier),r=[...this.desiredFeatures];r.sort(((e,t)=>a.P3[e.featureName]-a.P3[t.featureName])),r.forEach((r=>{if(!t[r.featureName]&&r.featureName!==a.K7.pageViewEvent)return;if(this.runSoftNavOverSpa&&r.featureName===a.K7.spa)return;if(!this.runSoftNavOverSpa&&r.featureName===a.K7.softNav)return;const n=function(e){switch(e){case a.K7.ajax:return[a.K7.jserrors];case a.K7.sessionTrace:return[a.K7.ajax,a.K7.pageViewEvent];case a.K7.sessionReplay:return[a.K7.sessionTrace];case a.K7.pageViewTiming:return[a.K7.pageViewEvent];default:return[]}}(r.featureName).filter((e=>!(e in this.features)));n.length>0&&(0,e.R)(36,{targetFeature:r.featureName,missingDependencies:n}),this.features[r.featureName]=new r(this)}))}catch(t){(0,e.R)(22,t);for(const e in this.features)this.features[e].abortHandler?.();const r=(0,h.Zm)();delete r.initializedAgents[this.agentIdentifier]?.api,delete r.initializedAgents[this.agentIdentifier]?.features,delete this.sharedAggregator;return r.ee.get(this.agentIdentifier).abort(),!1}}}({features:[A,T,j],loaderType:"lite"})})()})();</script> <meta name="viewport" content="width=device-width, initial-scale=1">  <link rel="dns-prefetch" href="//extend.vimeocdn.com" /> <link rel="preconnect" href="//extend.vimeocdn.com" /> <link rel="dns-prefetch" href="//cdnjs.cloudflare.com" /> <link rel="preconnect" href="//cdnjs.cloudflare.com" /> <link rel="dns-prefetch" href="//www.googletagmanager.com" /> <link rel="preconnect" href="//www.googletagmanager.com" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="shortcut icon" href="https://groups.oist.jp/sites/default/files/favicon.ico" type="image/vnd.microsoft.icon" /> <meta name="description" content="ABSTRACT The Gravity, Quantum Geometry and Field Theory Unit's research interest lies in quantum gravity. Quantizing gravity has been one of the most difficult problems in physics. There have been many approaches to quantizing gravity, which have given us mathematically and physically interesting ideas, such as the unification of forces, the emergence of spacetime, the problem" /> <meta name="generator" content="Drupal 7 (http://drupal.org)" /> <link rel="canonical" href="https://groups.oist.jp/qgqft" /> <link rel="shortlink" href="https://groups.oist.jp/node/21465" /> <meta property="og:site_name" content="OIST Groups" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://groups.oist.jp/qgqft" /> <meta property="og:title" content="Gravity, Quantum Geometry and Field Theory Unit (Reiko Toriumi)" /> <meta property="og:description" content="ABSTRACT The Gravity, Quantum Geometry and Field Theory Unit's research interest lies in quantum gravity. Quantizing gravity has been one of the most difficult problems in physics. There have been many approaches to quantizing gravity, which have given us mathematically and physically interesting ideas, such as the unification of forces, the emergence of spacetime, the problem of time, information paradox, spacetime foam, non-commutativity of spacetime, extra-dimensions like in Calabi-Yau manifold, duality, holography, etc." /> <meta property="og:updated_time" content="2022-02-09T16:59:42+09:00" /> <meta property="article:published_time" content="2018-11-08T16:56:13+09:00" /> <meta property="article:modified_time" content="2022-02-09T16:59:42+09:00" /> <title>Gravity, Quantum Geometry and Field Theory Unit (Reiko Toriumi) | OIST Groups</title> <link type="text/css" rel="stylesheet" href="/sites/default/files/advagg_css/css__rEEZSf_3bA2WGEhxDgcBbyjEWYY6p9lSkGZtKYzeg2c__LEjITr56B-Wb4wdQo-Lb-0jvkDyd3V53eoXOdT8iM4M__ARceOUK1yGXJaoZPgCjrfa7dNLgGccd9-Qt5-AQ9SjU.css" media="all" /> <link type="text/css" rel="stylesheet" href="/sites/default/files/advagg_css/css__AtZwdWqb3DimrNTt16QAgFVvTyvFzufIRfHNmiVJLuQ__VfbRKEbutORqImgqZ8iBvwZSTRRZe3baV3Y-rKDXRLI__ARceOUK1yGXJaoZPgCjrfa7dNLgGccd9-Qt5-AQ9SjU.css" media="all" /> <script src="/sites/default/files/advagg_js/js__xU_QDh50dsnCyA36pvXxs5mI1_GBgG3xWe3q_yEBGwI__XaTIQHhAW_Qhm3R-F1r8pC6GRpECix8dIj09neDXXZs__ARceOUK1yGXJaoZPgCjrfa7dNLgGccd9-Qt5-AQ9SjU.js" defer="defer"></script> <script src="/sites/default/files/advagg_js/js__vhL1XQaznZjnz51aQBqGRk0LYjY-clIPJUDnVQ-1u8o__16FAOU7kBs7ZYP0PjL4yngzH_1_5qpSu-i6wf3PxzIk__ARceOUK1yGXJaoZPgCjrfa7dNLgGccd9-Qt5-AQ9SjU.js"></script> <script src="/sites/default/files/advagg_js/js__GDg6JYgyqgadDzGb8RENyZ9WWusyqV5nDlBPKNhVQ4Q__I5hEKWuBzTOYF_BfClrj2YaHDz7W_JyjMQWLqt-Mzj0__ARceOUK1yGXJaoZPgCjrfa7dNLgGccd9-Qt5-AQ9SjU.js"></script> <script> <![CDATA[//><!]]> </script> <script src="/sites/default/files/advagg_js/js__KaZp60twaRFpB7IdN57N22C_sjMQDY1aEnvERtknlIg__qxx0tZ2oz4MKEStUB_CPRHqSQzyJ0TJSjo-52r5f8jw__ARceOUK1yGXJaoZPgCjrfa7dNLgGccd9-Qt5-AQ9SjU.js"></script> <script async="async" src="https://www.googletagmanager.com/gtag/js?id=UA-26875993-3"></script> <script> <![CDATA[//><!]]> </script> <script src="/sites/default/files/advagg_js/js__-enW62VtyGRsRljhj-6JYSCanRFB3vefxJngd5i9Ak8__TbLNFAWq2Tam9aW92k51wFqlDr-6pVmfdoJ34crptqY__ARceOUK1yGXJaoZPgCjrfa7dNLgGccd9-Qt5-AQ9SjU.js"></script> <script> <![CDATA[//><!]]> </script>   </head> <body class="html not-front not-logged-in no-sidebars page-node page-node- page-node-21465 node-type-group og-context og-context-node og-context-node-21465 i18n-en"> <a href="#content" class="skip">Skip to main content</a> <div id="print-logo"> <img src="/sites/all/themes/oistgroups2016/images/logo-print-en.png" class="print-logo-img logo-en" /> <img src="/sites/all/themes/oistgroups2016/images/logo-print-ja.png" class="print-logo-img logo-ja" /> </div> <noscript aria-hidden="true"><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PQD33H8" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div id="header"> <div id="header_line"></div> <div class="header-inner"> <div class="container"> <div class="row"> <div class="col first col-xs-6 col-sm-7"> <p> <a href="https://groups.oist.jp"><img class="hidden-xs hidden-sm hidden-md" role="img" id="logo" src="https://groups.oist.jp/sites/all/themes/oistgroups2016/images/oist-header-en.png" alt="Okinawa Institute of Science and Technology Graduate University Logotype" /></a> <a href="https://groups.oist.jp"><img class="visible-xs visible-sm visible-md" role="img" id="logo-mobile" src="https://groups.oist.jp/sites/all/themes/oistgroups2016/images/oist-header-en-mobile.png" alt="Okinawa Institute of Science and Technology Graduate University Logotype" /></a> </p> </div> <div class="col last col-xs-6 col-sm-5 text-right"> <div id="toggle-buttons" role="group"> <a href="#sidebar-left" class="navbar-toggle btn btn-default" type="button">Menu</a> <button data-target="#main-nav" data-toggle="collapse" class="navbar-toggle collapsed btn btn-default" type="button">Tools</button> </div> </div> </div> </div> </div> </div> <div id="main-nav-row" class="container"> <div class="row"> <div class="col-sm-12"> <nav id="main-nav" role="navigation" class="navbar navbar-default collapse navbar-collapse"> <ul class="main-menu nav navbar-nav"><li class="item1 first"><a href="https://groups.oist.jp">Groups</a></li> <li class="item2"><a href="https://www.oist.jp/">OIST</a></li> <li class="item3"><a href="http://search.oist.jp/">Search</a></li> <li class="item4"><a href="https://directory.oist.jp/">Directory</a></li> <li class="item5 last"><a href="/saml_login">Log in</a></li> </ul> <section id="block-locale-language" class="block block-locale clearfix"> <div class="item-list"><ul class="language-switcher-locale-url nav navbar-nav"><li class="active first"><a href="/qgqft" class="active">English</a></li> <li class="active last"><a href="/ja/qgqft">日本語</a></li> </ul></div></section> </nav> </div> </div> </div><div id="system"> <div> <section> </section> </div> </div> <div id="block-system-main" class="block block-system"> <div class="content"> <div id="main"> <div> <div> <div id="main-content"> <div class="field field-name-title-field field-type-text field-label-hidden"> <h1>Gravity, Quantum Geometry and Field Theory Unit (Reiko Toriumi)</h1> </div> <div id="myCarousel-178265" class="carousel slide carousel-178265" data-ride="carousel"> <div class="carousel-inner" role="listbox"> <div class="item active"><img src="https://groups.oist.jp/sites/default/files/styles/group_image/public/groups/banner_0.png?itok=ZjTiCr51" width="1170" height="186" alt="" /></div> </div> </div> <div class="field field-name-body field-type-text-with-summary field-label-hidden"> <p> </p> <h3><strong>ABSTRACT</strong></h3> <p>The Gravity, Quantum Geometry and Field Theory Unit's research interest lies in quantum gravity. Quantizing gravity has been one of the most difficult problems in physics. There have been many approaches to quantizing gravity, which have given us mathematically and physically interesting ideas, such as the unification of forces, the emergence of spacetime, the problem of time, information paradox, spacetime foam, non-commutativity of spacetime, extra-dimensions like in Calabi-Yau manifold, duality, holography, etc.</p> <p>Geometry, which initially found a link to gravity by Einstein's proposal, namely General Relativity, has also been playing a major role in the studies of quantum gravity. Geometrical aspects of gravity have been enjoyed by the advancement in the approaches to quantum gravity, such as matrix models, tensor models, lattice methods like causal dynamical triangulations and Regge calculus, etc.</p> <p>Quantum field theory (QFT), which gave us a tremendous success in describing the Standard Model including the weak, the strong and the electromagnetic forces, is also a central solid modern tool in describing physical systems with many degrees of freedom. QFT lets us explore critical phenomena and the scale dependence of the physics through the renormalization group.</p> <p>We combine these advanced tools in order to reveal the quantum nature of spacetime.</p> </div> <h2 class="pane-title"> Latest Posts </h2> <div id="post-listing"> <div class="view view-group-posts view-id-group_posts view-display-id-default view-dom-id-235e7368c3c642fd24fa56db488c5679"> <div class="item-list"> <ul> <li class="views-row views-row-1 views-row-odd views-row-first"> </li> <li class="views-row views-row-2 views-row-even views-row-last"> </li> </ul></div> <div class="more-link"> <a href="/qgqft/posts"> More Posts </a> </div> </div> </div> </div> <aside id="sidebar-left"> <section><nav id="sidebar-nav" role="navigation" class="navbar navbar-default"><ul class="nav nav-pills nav-stacked"><li class="first leaf"><a href="/qgqft" target="" title="" class="active">Top</a></li> <li class="expanded"><a href="/qgqft/members" target="" title="">Members</a><span class="glyphicon glyphicon-chevron-down dropdown-toggle" data-toggle="dropdown"></span><ul class="second dropdown-menu"><li class="first leaf"><a href="/qgqft/reiko-toriumi" target="" title="">Reiko Toriumi</a></li> <li class="leaf"><a href="https://groups.oist.jp/qgqft/nicolas-delporte" target="" title="">Nicolas Delporte</a></li> <li class="leaf"><a href="/qgqft/remi-avohou" target="" title="">Remi Avohou</a></li> <li class="leaf"><a href="/qgqft/cihan-pazarba%C5%9F%C4%B1" target="" title="">Cihan Pazarbaşı</a></li> <li class="leaf"><a href="/qgqft/rudrajit-banerjee" target="" title="">Rudrajit Banerjee</a></li> <li class="leaf"><a href="/qgqft/saswato-sen" target="" title="">Saswato Sen</a></li> <li class="leaf"><a href="/qgqft/andreani-petrou" target="" title="">Andreani Petrou</a></li> <li class="leaf"><a href="/qgqft/juan-luis-araujo-abranches" target="" title="">Juan Luis Araujo Abranches</a></li> <li class="leaf"><a href="https://groups.oist.jp/qgqft/giacomo-la-scala" target="" title="">Giacomo La Scala</a></li> <li class="last leaf"><a href="/qgqft/alumni" target="" title="">Alumni</a></li> </ul></li> <li class="leaf"><a href="/qgqft/posts" target="" title="">Unit News</a></li> <li class="leaf"><a href="/node/21465/events" target="" title="">Upcoming Events</a></li> <li class="collapsed"><a href="/node/21465/pastevents" target="" title="">Past Events</a></li> <li class="leaf"><a href="/qgqft/seminar" target="" title="">Seminars</a></li> <li class="leaf"><a href="/qgqft/journal-club" target="" title="">Journal Club</a></li> <li class="leaf"><a href="/node/21465/calendar" target="" title="">Calendar</a></li> <li class="leaf"><a href="/qgqft/fy2019-annual-report" target="" title="">FY2019 Annual Report</a></li> <li class="leaf"><a href="https://groups.oist.jp/qgqft/fy2020-annual-report" target="" title="">FY2020 Annual Report</a></li> <li class="leaf"><a href="/qgqft/fy2021-annual-report" target="" title="">FY2021 Annual Report</a></li> <li class="leaf"><a href="/qgqft/fy2022-annual-report" target="" title="">FY2022 Annual Report</a></li> <li class="leaf"><a href="/qgqft/open-positions" target="" title="">Open Positions</a></li> <li class="last leaf"><a href="https://www.oist.jp/research/research-units/qgqft/news" target="_blank" title="">OIST News Feed</a></li> </ul></nav></section> </aside> </div> </div> </div> </div> </div> <footer id="footer"> <div id="footer-primary"> <div> <div class="address"> <p>Okinawa Institute of Science and Technology Graduate University<br /> 1919-1 Tancha, Onna-son, Kunigami-gun<br /> Okinawa, Japan 904-0495<br /> <a href="https://www.oist.jp/contact-us">How to Contact OIST</a></p> </div> <div class="menu"> <ul class="links"><li class="item1 first"><a href="https://www.oist.jp/">Home</a></li> <li class="item2"><a href="https://www.oist.jp/about">About</a></li> <li class="item3"><a href="/grad">Graduate School</a></li> <li class="item4"><a href="https://www.oist.jp/research-overview">Research</a></li> <li class="item5"><a href="https://www.oist.jp/community-activities">Community</a></li> <li class="item6"><a href="https://groups.oist.jp/upcoming">Events</a></li> <li class="item7"><a href="https://www.oist.jp/news-center">News Center</a></li> <li class="item8 last"><a href="https://www.oist.jp/careers">Careers</a></li> </ul> </div> </div> </div> <div id="footer-secondary-wrapper"> <div id="footer-secondary"> <div> <div class="copyright">Copyright © 2024 Okinawa Institute of Science and Technology Graduate University</div> <div class="legal"> <ul class="links"><li class="item1 first"><a href="https://tida.oist.jp/">TIDA</a></li> <li class="item2"><a href="/acd/privacy-policy">Privacy Policy</a></li> <li class="item3 last"><a href="https://www.oist.jp/sitemap">Sitemap</a></li> </ul> </div> </div> </div> </div> </footer> <script defer="defer" src="https://extend.vimeocdn.com/ga/61626010.js"></script> <script src="//cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-AMS_HTML"></script> <script type="text/javascript">window.NREUM||(NREUM={});NREUM.info={"beacon":"bam.nr-data.net","licenseKey":"bae5605f02","applicationID":"273632920","transactionName":"YVxVMUZQCBVVBkNdW1gWYhddHkkPWgFSTBpGUUc=","queueTime":0,"applicationTime":384,"atts":"TRtWRw5KGxs=","errorBeacon":"bam.nr-data.net","agent":""}</script></body> </html>