Anomalies of the Entanglement Entropy in Chiral Theories

TL;DR

This paper investigates how gravitational and gauge anomalies affect entanglement entropy in various dimensions, revealing that anomalies cause frame-dependent entropy shifts linked to mode flux imbalances and boundary effects.

Contribution

It provides a detailed analysis of entanglement entropy anomalies in chiral theories, including explicit formulas and the role of index theorems and boundary conditions.

Findings

Anomalies cause frame-dependent shifts in entanglement entropy.

Mode flux imbalances explain the entanglement anomaly in symmetric cases.

Boundary anomalies manifest as entropy changes under metric shear.

Abstract

We study entanglement entropy in theories with gravitational or mixed U(1) gauge-gravitational anomalies in two, four and six dimensions. In such theories there is an anomaly in the entanglement entropy: it depends on the choice of reference frame in which the theory is regulated. We discuss subtleties regarding regulators and entanglement entropies in anomalous theories. We then study the entanglement entropy of free chiral fermions and self-dual bosons and show that in sufficiently symmetric situations this entanglement anomaly comes from an imbalance in the flux of modes flowing through the boundary, controlled by familiar index theorems. In two and four dimensions we use anomalous Ward identities to find general expressions for the transformation of the entanglement entropy under a diffeomorphism. (In the case of a mixed anomaly there is an alternative presentation of the theory in which the entanglement entropy is not invariant under a U(1) gauge transformation. The free-field manifestation of this phenomenon involves a novel kind of fermion zero mode on a gravitational background with a twist in the normal bundle to the entangling surface.) We also study d-dimensional anomalous systems as the boundaries of d + 1 dimensional gapped Hall phases. Here the full system is non-anomalous, but the boundary anomaly manifests itself in a change in the entanglement entropy when the boundary metric is sheared relative to the bulk.