Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals

TL;DR

This paper extends the holographic entanglement entropy framework to non-Lorentz invariant duals, proposing a new intrinsic method based on causal structures and null geodesics, with applications to warped CFTs and flat space.

Contribution

It introduces a novel prescription for gravitational entropy in non-Lorentz invariant spacetimes, differing from RT by using causal structure and null geodesics for regulation.

Findings

Calculated holographic entanglement entropy for warped CFTs.

Proposed a new intrinsic prescription for generalized gravitational entropy.

Applied the method successfully to flat space in three dimensions.

Abstract

Based on the Lewkowycz-Maldacena prescription and the fine structure analysis of holographic entanglement proposed in arXiv:1803.05552, we explicitly calculate the holographic entanglement entropy for warped CFT that duals to AdS$_3$ with a Dirichlet-Neumann type of boundary conditions. We find that certain type of null geodesics emanating from the entangling surface $\partial\mathcal{A}$ relate the field theory UV cutoff and the gravity IR cutoff. Inspired by the construction, we furthermore propose an intrinsic prescription to calculate the generalized gravitational entropy for general spacetimes with non-Lorentz invariant duals. Compared with the RT formula, there are two main differences. Firstly, instead of requiring that the bulk extremal surface $\mathcal{E}$ should be anchored on $\partial\mathcal{A}$, we require the consistency between the boundary and bulk causal structures to determine the corresponding $\mathcal{E}$. Secondly we use the null geodesics (or hypersurfaces) emanating from $\partial\mathcal{A}$ and normal to $\mathcal{E}$ to regulate $\mathcal{E}$ in the bulk. We apply this prescription to flat space in three dimensions and get the entanglement entropies straightforwardly.