Entanglement negativity, reflected entropy, and anomalous gravitation

TL;DR

This paper explores entanglement measures like negativity and reflected entropy in 2D conformal field theories with anomalies, proposing holographic duals involving topologically massive gravity and confirming their agreement with field theory calculations.

Contribution

It extends holographic proposals for entanglement negativity to include gravitational Chern-Simons terms and computes their effects on dual geometric quantities.

Findings

Exact agreement between field theory and holographic calculations.

Extension of holographic entanglement negativity to theories with gravitational anomalies.

New insights into the role of topologically massive gravity in entanglement measures.

Abstract

We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in AdS$_3$ and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute its contribution to the entanglement wedge cross section dual to the reflected entropy.