Document Zbl 1161.83343

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Phys.</a> <a href="/?q=in%3A247352" title="Articles in this Issue">324, No. 2, 414-469 (2009)</a>. </div> <div class="abstract">Summary: We review and extend in several directions recent results on the “asymptotic safety” approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian renormalization group equation. We begin by discussing various cutoff schemes, i.e. ways of implementing the Wilsonian cutoff procedure. We compare the beta functions of the gravitational couplings obtained with different schemes, studying first the contribution of matter fields and then the so-called Einstein-Hilbert truncation, where only the cosmological constant and Newton’s constant are retained. In this context we make connection with old results, in particular we reproduce the results of the epsilon expansion and the perturbative one-loop divergences. We then apply the Renormalization Group to higher derivative gravity. In the case of a general action quadratic in curvature we recover, within certain approximations, the known asymptotic freedom of the four-derivative terms, while Newton’s constant and of the cosmological constant have a nontrivial fixed point. In the case of actions that are polynomials in the scalar curvature of degree up to eight we find that the theory has a fixed point with three UV-attractive directions, so that the requirement of having a continuum limit constrains the couplings to lie in a three-dimensional subspace, whose equation is explicitly given. We emphasize throughout the difference between scheme-dependent and scheme-independent results, and provide several examples of the fact that only dimensionless couplings can have “universal” behavior.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5539151">Cited in <strong>130</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A83C45" title="MSC2020">83C45</a> </td> <td class="space"> Quantization of the gravitational field </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A83-02" title="MSC2020">83-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aquantum+gravity">quantum gravity</a>; <a href="/?q=ut%3Arenormalization+group">renormalization group</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1161.83343" data-ciurl="/ci/05539151" data-biburl="/bibtex/05539151.bib" data-amsurl="/amsrefs/05539151.bib" data-xmlurl="/xml/05539151.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05539151.pdf" title="Zbl 1161.83343 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.aop.2008.08.008" aria-label="DOI for “Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation”" title="10.1016/j.aop.2008.08.008">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/0805.2909"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Burgess, Cliff P., Living Rev. 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