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Guo, WZ; Miao, RX
Entropy for gravitational Chern-Simons terms by squashed cone method
KeywordAdS-CFT Correspondence MASSIVE GAUGE-THEORIES Classical Theories of Gravity BLACK-HOLES
AbstractIn this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D there is no anomaly of entropy. But the original squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation d Omega(4n-1) = tr(R-2n). We notice that the entropy of tr(R-2n) is a total derivative locally, i.e. S = ds(CS). We propose to identify s(CS) with the entropy of gravitational Chern-Simons terms Omega(4n-1). In the first method we could get the correct result for Wald entropy in arbitrary dimension. In the second approach, in addition to Wald entropy, we can also obtain the anomaly of entropy with non-zero extrinsic curvatures. Our results imply that the entropy of a topological invariant, such as the Pontryagin term tr(R-2n) and the Euler density, is a topological invariant on the entangling surface.
Subject AreaPhysics
Indexed BySCI
Funding OrganizationSino-Germann (CSC-DAAD) Postdoc Scholarship Program ; Postgraduate Scholarship Program of China Scholarship Council
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Document Type期刊论文
Affiliation1.Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Zhong Guan Cun East St 55,POB 2735, Beijing 100190, Peoples R China
2.Kyoto Univ, YITP, Sakyo Ku, Kyoto 6068502, Japan
3.Max Planck Inst Gravitat Phys, Albert Einstein Inst, Muhlenberg 1, D-14476 Golm, Germany
Recommended Citation
GB/T 7714
Guo, WZ,Miao, RX. Entropy for gravitational Chern-Simons terms by squashed cone method[J]. JOURNAL OF HIGH ENERGY PHYSICS,2016(4):6.
APA Guo, WZ,&Miao, RX.(2016).Entropy for gravitational Chern-Simons terms by squashed cone method.JOURNAL OF HIGH ENERGY PHYSICS(4),6.
MLA Guo, WZ,et al."Entropy for gravitational Chern-Simons terms by squashed cone method".JOURNAL OF HIGH ENERGY PHYSICS .4(2016):6.
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