English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Entropy for gravitational Chern-Simons terms by squashed cone method

MPS-Authors
/persons/resource/persons127852

Miao,  Rong Xin
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

External Ressource
No external resources are shared
Fulltext (public)

1506.08397.pdf
(Preprint), 217KB

JHEP04(2016)006.pdf
(Publisher version), 464KB

Supplementary Material (public)
There is no public supplementary material available
Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0028-1DFF-D
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.