Anomalies and Entanglement Entropy

TL;DR

This work analyzes how gauge and gravitational anomalies modify entanglement and Rényi entropies in even-dimensional QFTs. Using the replica trick and anomaly inflow, it derives a general boost-variation formula for Rényi entropy, linking the θ-derivative to anomaly-induced non-conservation terms and Chern-Simons data. It provides explicit results in 2D, 4D, and 6D (and a general higher-dimensional framework), showing that the entanglement entropy can acquire imaginary, anomaly-determined contributions in the presence of external fields or nontrivial topology. The findings reveal that entanglement entropy encodes detailed information about gravitational and mixed anomalies, with the precise outcome depending on Bardeen counterterms and boundary effects, and offer avenues for holographic checks and studies of anomaly-induced entanglement structures in higher dimensions.

Abstract

We initiate a systematic study of entanglement and Renyi entropies in the presence of gauge and gravitational anomalies in even-dimensional quantum field theories. We argue that the mixed and gravitational anomalies are sensitive to boosts and obtain a closed form expression for their behavior under such transformations. Explicit constructions exhibiting the dependence of entanglement entropy on boosts is provided for theories on spacetimes with non-trivial magnetic fluxes and (or) non-vanishing Pontryagin classes.