Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution

TL;DR

This paper calculates the universal vertex contribution to the logarithmic divergence in entanglement entropy for a free Dirac fermion in three dimensions, extending previous scalar field results and linking to conformal anomalies.

Contribution

It provides the first explicit computation of the vertex contribution for a Dirac fermion in three dimensions, generalizing earlier scalar field findings.

Findings

Derived the universal coefficient for Dirac fermions

Extended scalar case results to fermionic fields

Connected entanglement entropy divergence to conformal anomalies

Abstract

In three dimensions there is a logarithmically divergent contribution to the entanglement entropy which is due to the vertices located at the boundary of the region considered. In this work we find the corresponding universal coefficient for a free Dirac field, and extend a previous work in which the scalar case was treated. The problem is equivalent to find the conformal anomaly in three dimensional space where multiplicative boundary conditions for the field are imposed on a plane angular sector. As an intermediate step of the calculation we compute the trace of the Green function of a massive Dirac field in a two dimensional sphere with boundary conditions imposed on a segment of a great circle.