Fermionic determinant with a linear domain wall in 2+1 dimensions

TL;DR

This paper computes the exact fermionic determinant for a Dirac field in 2+1 dimensions with a linear domain wall and a constant electromagnetic field, analyzing geometric dependencies and vacuum energy implications.

Contribution

It provides an exact evaluation of the fermionic determinant in a novel setup involving a linear domain wall and electromagnetic field in 2+1 dimensions.

Findings

Determinant depends on the relative orientation of the wall and external field.

Explicit expression for the fermionic determinant in the presence of a domain wall.

Application to vacuum energy calculation.

Abstract

We consider a Dirac field in 2+1 Euclidean dimensions, in the presence of a linear domain wall defect in its mass, and a constant electromagnetic field. We evaluate the exact fermionic determinant for the situation where the defect is assumed to be rectilinear, static, and the gauge field is minimally coupled to the fermions. We discuss the dependence of the result on the (unique) independent geometrical parameter of this system, namely, the relative orientation of the wall and the direction of the external field. We apply the result for the determinant to the evaluation of the vacuum energy.