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

Abstract

We evaluate quantum effects due to a two-component Dirac field in 2+1 spacetime dimensions, coupled to domain-wall-like defects with a smooth shape. We show that these effects induce nontrivial 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 nontrivial, Casimir-like effect between them, and we 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.