In this work, we study the holographic entanglement entropy in AdS3 gravity with the certain mixed boundary condition, which turns out to correspond to TT¯-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in TT¯-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both TT¯-deformed CFTs and cutoff AdS3. Moreover, our result shows that the deformed entanglement entropy for large deformation parameter behaves like the entanglement entropy of CFT at zero temperature. We also consider the entanglement entropy of two intervals and study the effect of TT¯ deformation on phase transition.
In this work, we study the holographic entanglement entropy in AdS3 gravity with the certain mixed boundary condition, which turns out to correspond to TT¯-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in TT¯-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both TT¯-deformed CFTs and cutoff AdS3. Moreover, our result shows that the deformed entanglement entropy for large deformation parameter behaves like the entanglement entropy of CFT at zero temperature. We also consider the entanglement entropy of two intervals and study the effect of TT¯ deformation on phase transition.
A holographic correspondence has been recently developed between higher spin theories in three-dimensional anti-de Sitter space (AdS3) and two-dimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N, R) × SL(N, R) Chern-Simons gauge theories in the (2 + 1)-dimensional bulk space-time, and CFTs with WN symmetry algebras on the (1 + 1)-dimensional boundary. The topological character of the bulk theory forces one to reconsider standard geometric notions such as black hole horizons and entropy, as well as the usual holographic dictionary. Motivated by this challenge, in this note we present a proposal to compute entanglement entropy in the WN CFTs via holographic methods. In particular, we introduce a functional constructed from Wilson lines in the bulk Chern-Simons theory that captures the entanglement entropy in the CFTs dual to standard AdS3 gravity, corresponding to SL(2, R) × SL(2, R) gauge group, and admits an immediate generalization to the higher spin case. We explicitly evaluate this functional for several known solutions of the bulk theory, including charged black holes dual to thermal CFT states carrying higher spin charge, and show that it reproduces expected features of entanglement entropy, study whether it obeys strong subadditivity, and moreover show that it reduces to the thermal entropy in the appropriate limit.
In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional TT-deformed conformal field theory (CFT). For such case, the (R\'enyi) entanglement entropy takes a universal form in a CFT. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of the conformal perturbation theory. We find that the correction to the entanglement entropy is nonvanishing in the finite temperature case, while it is vanishing in the finite size case. For the deformed holographic large c CFT, which is proposed to be dual to a AdS3 gravity in a finite region, we find the agreement with the holographic entanglement entropy via the Ryu-Takayanagi formula. Moreover, we compute the leading order correction to the R\'enyi entropy, and discuss its holographic picture as well.
We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential μ for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in μ in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3, ℝ) × SL(3, ℝ) Chern-Simons theory. Our result suggests that the order μ 2 correction to the entanglement entropy may be universal for $ \mathcal{W} $ -algebra CFTs with spinthree chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS3.
Abstract In this paper we study the entanglement entropy in the CFT2, whose gravity dual is AdS3 spacetime with a Chern-Simons term. Using the generalized Rindler method, we obtain the Rindler transformation in the two-dimensional planar CFT and compute the entanglement entropy of the CFT with gravitational anomalies. The conditions under which the entanglement entropy may have anomalous contributions is also discussed. In addition, we present a relatively general form of the Rindler AdS metric and compute its thermal entropy, which agrees with the entanglement entropy in the field theory. Moreover, we utilize the conformal transformation, which maps a cylinder to a plane, to compute the entanglement entropy of the CFT residing on a cylinder, as well as the entanglement entropy of the CFT at finite temperature on a plane. The corresponding contribution of the Chern-Simons term in gravity to the black hole thermal entropy is also obtained from this approach. These results are important for further understandings of the two-dimensional CFT with gravitational anomalies.
We study two-interval holographic entanglement entropy and entanglement wedge cross section in cutoff AdS. In particular, we investigate phase transitions of them. For two-interval entanglement entropy, the transition point monotonically decreases with a deformation parameter, which means that by the TT deformation the degrees of freedom in subsystems are decreasing. This implies that the effect of the TT deformation can be regarded as the rescaling of the energy scale. We also study entanglement wedge cross section in cutoff AdS, and our result implies that for the entanglement of purification in the TT deformed CFTs phase transition could occur even for fixed subsystems.
We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential mu for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in mu in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3, R) x SL(3, R) Chern-Simons theory. Our result suggests that the order mu(2) correction to the entanglement entropy may be universal for W-algebra CFTs with spin-three chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS(3).