Domain wall interactions due to vacuum Dirac field fluctuations in 2+1 dimensions

TL;DR

This paper investigates quantum effects of a Dirac field in 2+1 dimensions interacting with domain walls, revealing shape-dependent energies, divergences, zero modes, and Casimir-like interactions between defects.

Contribution

It provides a detailed analysis of quantum vacuum effects on domain walls in 2+1 dimensions, including exact expressions for defect interactions and the role of zero modes.

Findings

Quantum effects induce shape-dependent energy contributions.

Divergences in self-energy are analyzed and addressed.

Exact Casimir-like interaction energy is derived for parallel defects.

Abstract

We evaluate quantum effects due to a $2$-component Dirac field in $2+1$ space-time dimensions, coupled to domain-wall like defects with a smooth shape. We show that those effects induce non trivial contributions to the (shape-dependent) energy of the domain walls. For a single defect, we study the divergences in the corresponding self-energy, and also consider the role of the massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling the Dirac field to an external gauge field. For two defects, we show that the Dirac field induces a non trivial, Casimir-like effect between them, and provide an exact expression for that interaction in the case of two straight-line parallel defects. As is the case for the Casimir interaction energy, the result is finite and unambiguous.