Holographic Rényi entropy in AdS3/LCFT2 correspondence

Abstract

The recent study in AdS 3 /CFT 2 correspondence shows that the tree level contribution and 1-loop correction of holographic Rényi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the Rényi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of Rényi 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 Rényi 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.

On the mutual information in conformal field theory

“…Especially for the large c CFT dual to the AdS 3 gravity, the vacuum module contribution dominates the partition function in the large central charge limit. This leads to a lot of study on the two-interval Rényi entropy in the large c CFTs, which sheds new light on the AdS 3 /CFT 2 correspondence [28][29][30][31][32][33][34][35][36]. Some relevant discussions on entanglement entropy of 2D quantum field theory can be found in [37][38][39][40][41][42][43][44][45][46][47].…”

Thermality and excited state Rényi entropy in two-dimensional CFT

“…After that, one can obtain the short-interval expansion of the Rényi entropy by evaluating the corresponding one-point or multi-point functions of the OPE blocks. This trick has been adopted to calculate the Rényi entropy for some special cases [11][12][13][14][15][16][17][18][19][20], such as the Rényi entropy of two intervals on complex plane and of the one-interval on torus. In this paper, we adopt the same trick to investigate the short-interval expansion of excited state Rényi entropy on a cylinder, and then compare our results with the thermal state Rényi entropy.…”

Conformal blocks and negativity at large central charge

“…the spectrum of the operators and the OPE coefficients [20] (see also [21][22][23][24] and for related work [25][26][27][28][29]). One may ask whether a similar approach can be useful in the computation of entanglement negativity, and if the holographic prescription can be inferred from it.…”