One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization

TL;DR

This paper introduces an adapted dimensional regularization approach to compute one-loop quantum corrections to kink domain walls' surface tensions, simplifying calculations and providing new results for supersymmetric cases.

Contribution

The paper presents a novel dimensional regularization method that simplifies one-loop calculations of surface tensions in kink domain walls, including supersymmetric models.

Findings

Derived a compact d-dimensional formula for quantum mass and surface tension.

Successfully calculated one-loop correction for 2+1D N=1 supersymmetric kink domain wall.

Reproduced many previous results with a simplified approach.

Abstract

We consider domain walls obtained by embedding the 1+1-dimensional $\phi^4$-kink in higher dimensions. We show that a suitably adapted dimensional regularization method avoids the intricacies found in other regularization schemes in both supersymmetric and non-supersymmetric theories. This method allows us to calculate the one-loop quantum mass of kinks and surface tensions of kink domain walls in a very simple manner, yielding a compact d-dimensional formula which reproduces many of the previous results in the literature. Among the new results is the nontrivial one-loop correction to the surface tension of a 2+1 dimensional N=1 supersymmetric kink domain wall with chiral domain-wall fermions.