Abstract
The study of Rényi mutual information (RMI) sheds light on the AdS/CFT correspondence beyond classical order. In this article, we study the Rényi mutual in- formation between two intervals at large distance in two-dimensional holographic warped conformal field theory, which is conjectured to be dual to gravity on AdS3 or warped AdS3 spacetimes under Dirichlet-Neumann boundary conditions. By using the operator product expansion of twist operators up to level 3, we read the leading oder and the next-to-leading order RMI in the large central charge and small cross-ratio limits. The leading order result is furthermore confirmed using the conformal block expansion. Finally, we match the next-to-leading order result by a 1-loop calculation in the bulk.
Highlights
It has been shown in [6] that the holographic entanglement entropy can be taken as a kind of generalized gravitational entropy and it can be computed by the classical action of the corresponding gravitational configuration
We study the Renyi mutual information between two intervals at large distance in two-dimensional holographic warped conformal field theory, which is conjectured to be dual to gravity on AdS3 or warped AdS3 spacetimes under Dirichlet-Neumann boundary conditions
On the field theory side, assuming that the conformal block is dominated by the vacuum module at large c, one may use the recursive relation of the Virasoro block [12] or the operator product expansion (OPE) of the twist operators [18,19,20] to compute the correlation functions of the twist operators
Summary
We provide a brief review of warped CFTs [36, 41], starting with a definition on a Lorentzian cylinder, instead of the plane. We can define a reference cylinder with zero U(1) charge, and a spatial circle (x, y ) ∼ (x + 2π, y − 2πiμ). We can make a smooth cover of the reference cylinder by multiplying the circle by n while keeping the direction invariant. The smooth cover of the reference plane C is made by multiplying the circle by n while keeping the direction invariant, points will be identified as (z, y ) ∼ (ze2πni, y − 2πinμ). This property will help us understand the uniformazation map (3.10). The physical cylinder can be mapped to the canonical cylinder with a rescaling and tilting, and mapped to the canonical plane or the reference plane
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