Modifications to holographic entanglement entropy in warped CFT

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114

301

BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reformulate the Rindler method for calculating entanglement entropy in a general setup, and apply it for BMS invariant field theories, and finally extend the calculation to the bulk.

Section: Jhep07(2017)142mentioning

confidence: 53%

Section: The Strategymentioning

confidence: 75%

Section: Jhep07(2017)142mentioning

confidence: 99%

See 1 more Smart Citation

Entanglement entropy in flat holography

Jiang

Song

Wen

2017

Self Cite

114

301

“…17 It is remarkable that the final result is holomorphic as expected from (4.14). We stress that in a WCFT, suitable warped modular transformations also relate thermal AdS and BTZ [19,39]. This relationship explains why we obtain a vacuum character when evaluating the determinant on BTZ.…”

Section: Css Boundary Conditionsmentioning

confidence: 61%

Tweaking one-loop determinants in AdS3

Castro

Keeler

Szepietowski

2017

Abstract:We revisit the subject of one-loop determinants in AdS 3 gravity via the quasinormal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for the metric field; chirality is achieved by imposing Dirichlet boundary conditions on certain components while others satisfy Neumann. Along the way, we give a generalization of the quasinormal mode method for stationary (non-static) thermal backgrounds, and propose a treatment for Neumann boundary conditions in this framework. We evaluate the graviton one-loop determinant on the Euclidean BTZ background with parity-violating boundary conditions (CSS), and find excellent agreement with the dual warped CFT. We also discuss a more general falloff in AdS 3 that is related to two dimensional quantum gravity in lightcone gauge. The behavior of the ghost fields under both sets of boundary conditions is novel and we discuss potential interpretations.

“…G N is the Newton constant in d dimensions. S EE (A) satisfying RT formula is referred to as the holographic entanglement entropy (HEE) [16][17][18][19][20][21][22] The tensor network can be understood as a discrete version of the AdS/CFT correspondence [23][24][25][26][27][28][29][30]. The tensor network states approximates the CFT state at the boundary, while the structure of tensor network emerges an bulk dimension built by layers of tensors.…”

Section: Jhep11(2017)148mentioning

confidence: 99%

Discrete gravity on random tensor network and holographic Rényi entropy

Han

Huang

2017

In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy S n of |Ψ approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS 3 /CFT 2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.