Modular Hamiltonians and large diffeomorphisms in $AdS_3$

TL;DR

This paper extends the intersecting modular Hamiltonian approach to reconstruct bulk scalar fields in any locally $AdS_3$ space related by large diffeomorphisms, verifying consistency with known results and gravitational dressing corrections.

Contribution

It generalizes the modular Hamiltonian reconstruction method to a broader class of $AdS_3$ geometries connected by large diffeomorphisms, including gravitational dressing effects.

Findings

Matching with previous results in appropriate limits

Consistency with bulk diffeomorphisms

Computed first correction due to gravitational dressing

Abstract

We generalize the work of Kabat and Lifshytz (arXiv:1703.06523), of reconstructing bulk scalar fields using the intersecting modular hamiltonian approach discussed therein, to any locally $AdS_3$ space related to $AdS_3$ by large diffeomorphisms. We present several checks for our result including matcing with their result in appropriate limits as well as consistency with bulk diffeomorphisms. As a further check, from our expressions we also compute the first correction due to gravitational dressing to the bulk scalar field in $AdS_3$ and match with known results in the literature.