Holographic Renyi entropy in AdS$_3$/LCFT$_2$ correspondence

Chen, Bin; Song, Feng-yan; Zhang, Jia-ju

doi:10.1007/JHEP03(2014)137

Holographic Renyi entropy in AdS $_3$ /LCFT $_2$ correspondence

Bin Chen
(
- Peking U. and
- Unlisted, CN and
- Peking U., CHEP and
- Peking U., SKLNPT
)
,
Feng-yan Song
(
- Peking U. and
- Peking U., SKLNPT
)
,
Jia-ju Zhang
(
- Peking U. and
- Peking U., SKLNPT
)

Jan 1, 2014

27 pages

Published in:

JHEP 03 (2014) 137

Published: 2014

e-Print:

1401.0261 [hep-th]

DOI:

10.1007/JHEP03(2014)137

View in:

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Abstract: (arXiv)

The recent study in AdS

_3

/CFT

_2

correspondence shows that the tree level contribution and 1-loop correction of holographic R\'enyi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the R\'enyi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of R\'enyi entanglement entropy in pure AdS

_3

gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the R\'enyi entanglement entropy of two disjoint intervals with small cross ratio

x

, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order

x^6

. To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS

_3

gravity.

Note:

28 pages. Typos corrected, published version

Field Theories in Lower Dimensions
AdS-CFT Correspondence
Conformal and W Symmetry
field theory: conformal
entropy: entanglement
gravitation: massive
graviton: massless
anti-de Sitter
critical phenomena
duality

References(60)

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