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(PDF) Vortices in a nonminimal Maxwell–Chern–Simons O(3) sigma model
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{"work":{"id":31699793,"created_at":"2017-03-03T13:00:10.705-08:00","from_world_paper_id":161146561,"updated_at":"2025-01-11T23:54:13.156-08:00","_data":{"ai_abstract":"In this work, an Abelian O(3) sigma model is considered, coupled non-minimally with a gauge field governed by Maxwell and Chern-Simons terms. Bogomol'nyi equations are constructed for a specific form of the potential and a generic non-minimal coupling constant. Topological and nontopological self-dual solutions are obtained for a critical value of the non-minimal coupling constant. Particular static vortex solutions satisfying the Bogomol'nyi bound are numerically solved and presented.","publication_date":"2000,,","publication_name":"Physics Letters B"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Vortices in a nonminimal Maxwell–Chern–Simons O(3) sigma model","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [60898253]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":52015352,"attachmentType":"pdf"}"><img alt="First page of “Vortices in a nonminimal Maxwell–Chern–Simons O(3) sigma model”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/52015352/mini_magick20190123-29409-pxrapk.png?1548304756" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Vortices in a nonminimal Maxwell–Chern–Simons O(3) sigma model</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="60898253" href="https://bnfghhtrhtbnhfdhtryht.academia.edu/FranciscoCavalcante"><img alt="Profile image of Francisco Cavalcante" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Francisco Cavalcante</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2000, Physics Letters B</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">19 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 31699793; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--detail ds2-5-body-md">AI-generated Abstract</p><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">In this work, an Abelian O(3) sigma model is considered, coupled non-minimally with a gauge field governed by Maxwell and Chern-Simons terms. Bogomol'nyi equations are constructed for a specific form of the potential and a generic non-minimal coupling constant. Topological and nontopological self-dual solutions are obtained for a critical value of the non-minimal coupling constant. Particular static vortex solutions satisfying the Bogomol'nyi bound are numerically solved and presented.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":52015352,"attachmentType":"pdf","workUrl":"https://www.academia.edu/31699793/Vortices_in_a_nonminimal_Maxwell_Chern_Simons_O_3_sigma_model"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":52015352,"attachmentType":"pdf","workUrl":"https://www.academia.edu/31699793/Vortices_in_a_nonminimal_Maxwell_Chern_Simons_O_3_sigma_model"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas" data-impression-entity-id="31699793" data-impression-entity-type="2" data-impression-source="signup-banner"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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href="https://www.academia.edu/101584063/Z_flux_line_lattices_and_self_dual_equations_in_the_standard_model">Z flux-line lattices and self-dual equations in the standard model</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="36125861" href="https://izt-uam.academia.edu/GabrielVargasLozano">Gabriel Vargas Lozano</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review D, 1994</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Z flux-line lattices and self-dual equations in the standard model","attachmentId":102085345,"attachmentType":"pdf","work_url":"https://www.academia.edu/101584063/Z_flux_line_lattices_and_self_dual_equations_in_the_standard_model","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/101584063/Z_flux_line_lattices_and_self_dual_equations_in_the_standard_model"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="47456248" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/47456248/Vortices_in_He_II_current_algebras_and_quantum_knots">Vortices in He II, current algebras and quantum knots</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="65433989" href="https://independent.academia.edu/MarioRasetti">Mario Rasetti</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 1975</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Vortices in He II, current algebras and quantum knots","attachmentId":66539972,"attachmentType":"pdf","work_url":"https://www.academia.edu/47456248/Vortices_in_He_II_current_algebras_and_quantum_knots","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/47456248/Vortices_in_He_II_current_algebras_and_quantum_knots"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="114165376" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/114165376/Fractional_vortices_mml_math_xmlns_mml_http_www_w3_org_1998_Math_MathML_mml_msub_mml_mi_mathvariant_double_struck_Z_mml_mi_mml_mn_2_mml_mn_mml_msub_mml_math_gauge_theory_and_the_confinement_deconfinement_transition">Fractional vortices, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> gauge theory, and the confinement-deconfinement transition</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33150001" href="https://berkeley.academia.edu/DunghaiLee">Dung-hai Lee</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review, 2022</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we discuss the classical 3D XY model whose nearest-neighbor interaction is a mixture of cos(θi − θj) (ferromagnetic) and cos 2(θi − θj) (nematic). This model is dual to a theory with integer and half-integer vortices. While both types of vortices interact with a non-compact U(1) gauge field, the half-integer vortices interact with an extra interaction mediated by a Z2 gauge field. We shall discuss the confinement-deconfinement transition of the half-integer vortices, the Wilson and the 't Hooft loops and their mutual statistics in path integral language. In addition, we shall present a quantum version of the classical model which exhibits these physics.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fractional vortices, \u003cmml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmml:msub\u003e\u003cmml:mi mathvariant=\"double-struck\"\u003eZ\u003c/mml:mi\u003e\u003cmml:mn\u003e2\u003c/mml:mn\u003e\u003c/mml:msub\u003e\u003c/mml:math\u003e gauge theory, and the confinement-deconfinement transition","attachmentId":110934733,"attachmentType":"pdf","work_url":"https://www.academia.edu/114165376/Fractional_vortices_mml_math_xmlns_mml_http_www_w3_org_1998_Math_MathML_mml_msub_mml_mi_mathvariant_double_struck_Z_mml_mi_mml_mn_2_mml_mn_mml_msub_mml_math_gauge_theory_and_the_confinement_deconfinement_transition","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/114165376/Fractional_vortices_mml_math_xmlns_mml_http_www_w3_org_1998_Math_MathML_mml_msub_mml_mi_mathvariant_double_struck_Z_mml_mi_mml_mn_2_mml_mn_mml_msub_mml_math_gauge_theory_and_the_confinement_deconfinement_transition"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="16238190" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/16238190/Chern_Simons_vortices_in_the_Gudnason_model">Chern–Simons vortices in the Gudnason model</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35504144" href="https://independent.academia.edu/XiaosenHan">Xiaosen Han</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35334044" href="https://independent.academia.edu/GTarantello">G. Tarantello</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35417730" href="https://independent.academia.edu/ChangshouLin">Chang-shou Lin</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35503872" href="https://independent.academia.edu/YangYisong">Yisong Yang</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Functional Analysis, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the N = 2 supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern-Simons dynamics at dual levels and realized as the solutions of a system of elliptic equations with exponential nonlinearity over two-dimensional domains. In the full plane situation, our method utilizes a minimization approach, and in the doubly periodic situation, we employ an-inequality constrained minimization approach. In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices. In other words, there are distinct solutions with identical vortex distribution, energy, and electric and magnetic charges.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Chern–Simons vortices in the Gudnason model","attachmentId":42623179,"attachmentType":"pdf","work_url":"https://www.academia.edu/16238190/Chern_Simons_vortices_in_the_Gudnason_model","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/16238190/Chern_Simons_vortices_in_the_Gudnason_model"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="95900964" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/95900964/The_Gelfand_Mathematical_Seminars_1993_1995">The Gelfand Mathematical Seminars, 1993–1995</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="241426" href="https://rutgers.academia.edu/VladimirRetakh">Vladimir Retakh</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1996</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Gelfand Mathematical Seminars, 1993–1995","attachmentId":97951497,"attachmentType":"pdf","work_url":"https://www.academia.edu/95900964/The_Gelfand_Mathematical_Seminars_1993_1995","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/95900964/The_Gelfand_Mathematical_Seminars_1993_1995"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":52015352,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":52015352,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_52015352" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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ds2-5-body-sm ds2-5-body-link" data-author-id="218259684" href="https://independent.academia.edu/MarconyCunha">Marcony Cunha</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Modern Physics A, 1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Self-Dual Vortices in a Maxwell Chern–Simons Model with Nonminimal Coupling","attachmentId":85718878,"attachmentType":"pdf","work_url":"https://www.academia.edu/78802203/Self_Dual_Vortices_in_a_Maxwell_Chern_Simons_Model_with_Nonminimal_Coupling","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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ds2-5-body-xs">1994</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Self-Dual Charged Vortices of Finite Energy per Unit Length in $3+1$ Dimensions","attachmentId":72941068,"attachmentType":"pdf","work_url":"https://www.academia.edu/58616123/Self_Dual_Charged_Vortices_of_Finite_Energy_per_Unit_Length_in_3_1_Dimensions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/58616123/Self_Dual_Charged_Vortices_of_Finite_Energy_per_Unit_Length_in_3_1_Dimensions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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