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  Entropy for gravitational Chern-Simons terms by squashed cone method

Guo, W.-Z., & Miao, R. X. (2016). Entropy for gravitational Chern-Simons terms by squashed cone method. Journal of high energy physics: JHEP, 2016(04): 006. doi:10.1007/JHEP04(2016)006.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0028-1DFF-D Version Permalink: http://hdl.handle.net/21.11116/0000-0002-EC9D-4
Genre: Journal Article

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 Creators:
Guo, Wu-Zhong, Author
Miao, Rong Xin1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
 Abstract: In 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 we find no anomaly of entropy appears. But the 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 $d\bm{\Omega_{4n-1}}=tr(\bm{R}^{2n})$. We notice that the entropy of $tr(\bm{R}^{2n})$ is a total derivative locally, i.e. $S=d s_{CS}$. 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 $tr(\bm{R}^{2n})$ and the Euler density, is a topological invariant on the entangling surface.

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 Dates: 2015-06-282015-07-102016
 Publication Status: Published in print
 Pages: 19 page
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 Rev. Method: -
 Identifiers: arXiv: 1506.08397
URI: http://arxiv.org/abs/1506.08397
DOI: 10.1007/JHEP04(2016)006
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Title: Journal of high energy physics : JHEP
Source Genre: Journal
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Publ. Info: Bologna, Italy : Società italiana di fisica
Pages: - Volume / Issue: 2016 (04) Sequence Number: 006 Start / End Page: - Identifier: ISSN: 1126-6708
CoNE: https://pure.mpg.de/cone/journals/resource/111021927548002