Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT$_2$s and holography

TL;DR

This paper develops a perturbative replica technique to compute odd entanglement entropy in TT deformed CFT2s, connecting field theory results with holographic duals involving finite cut-off BTZ geometries.

Contribution

It introduces a novel perturbative method for calculating odd entanglement entropy in TT deformed CFT2s and links these results with holographic entanglement wedge cross sections.

Findings

Leading order corrections to OEE for various intervals in deformed CFT2s are computed.

Holographic calculations match field theory results in the high temperature limit.

Finite size, zero temperature corrections to OEE vanish at leading order in both approaches.

Abstract

We construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in $\text{T}\bar{\text{T}}$ deformed CFT$_2$s. This framework is then utilized to obtain the leading order correction to the OEE for two disjoint intervals, two adjacent intervals, and a single interval in $\text{T}\bar{\text{T}}$ deformed thermal CFT$_2$s in the large central charge limit. The field theory results are subsequently reproduced in the high temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cut-off BTZ geometries. We further show that for finite size $\text{T}\bar{\text{T}}$ deformed CFT$_2$s at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.