Entanglement Entropy & Anomaly Inflow

TL;DR

This paper investigates how entanglement entropy in parity-violating 3D quantum field theories is affected by Lorentz boosts, revealing a bulk-boundary entanglement inflow mechanism linked to gravitational anomalies.

Contribution

It demonstrates that bulk entanglement entropy cancels the boost sensitivity of boundary CFTs with gravitational anomalies, establishing a bulk-boundary entanglement inflow framework.

Findings

Bulk entanglement entropy cancels boundary boost effects.

Entanglement inflow links gravitational anomalies to entanglement spectrum.

Results apply to 2+1D topological phases with anomalous edge theories.

Abstract

We study entanglement entropy for parity-violating (time-reversal breaking) quantum field theories on $\mathbb{R}^{1,2}$ in the presence of a domain wall between two distinct parity-odd phases. The domain wall hosts a 1+1-dimensional conformal field theory (CFT) with non-trivial chiral central charge. Such a CFT possesses gravitational anomalies. It has been shown recently that, as a consequence, its intrinsic entanglement entropy is sensitive to Lorentz boosts around the entangling surface. Here, we show using various methods that the entanglement entropy of the three-dimensional bulk theory is also sensitive to such boosts owing to parity-violating effects, and that the bulk response to a Lorentz boost precisely cancels the contribution coming from the domain wall CFT. We argue that this can naturally be interpreted as entanglement inflow (i.e., inflow of entanglement entropy analogous to the familiar Callan-Harvey effect) between the bulk and the domain-wall, mediated by the low-lying states in the entanglement spectrum. These results can be generally applied to 2+1-d topological phases of matter that have edge theories with gravitational anomalies, and provide a precise connection between the gravitational anomaly of the physical edge theory and the low-lying spectrum of the entanglement Hamiltonian.