On the logarithmic coefficient of the entanglement entropy of a Maxwell field

TL;DR

This paper investigates the discrepancy between the A-anomaly coefficient and the logarithmic term in the entanglement entropy of a Maxwell field, revealing the role of superselection sectors, charges, and monopoles in this context.

Contribution

It demonstrates how superselection sectors and the presence of electric and magnetic charges affect the entanglement entropy's logarithmic term and restores the anomaly coefficient.

Findings

The logarithmic term differs for free and interacting Maxwell fields.

Coupling with charged vacuum fluctuations restores the anomaly coefficient.

Results are invariant under electromagnetic duality.

Abstract

We elucidate the mismatch between the $A$-anomaly coefficient and the coefficient of the logarithmic term in the entanglement entropy of a Maxwell field. In contrast to the usual assumptions about the protection of renormalization group charges at the infrared, the logarithmic term is different for a free Maxwell field and a Maxwell field interacting with heavy charges. This is possible because of the presence of superselection sectors in the IR theory. However, the correction due to the coupling with charged vacuum fluctuations, that restores the anomaly coefficient, is independent of the precise UV dynamics. The problem is invariant under electromagnetic duality, and the solution requires both the existence of electric charges and magnetic monopoles. We use a real-time operator approach but we also show how the results for the free and interacting fields are translated into an effective correction to the four-sphere partition function.