Scheme Dependence of the One-Loop Domain Wall Tension

TL;DR

This paper compares different methods for calculating the one-loop tension of domain walls in a scalar field theory, emphasizing the importance of the renormalization scheme for consistent results.

Contribution

It demonstrates that spectral methods and linearized perturbation theory yield consistent domain wall tension results when using the same renormalization scheme.

Findings

Spectral methods agree with previous results when renormalization schemes match.

Linearized soliton perturbation theory produces compatible tension calculations.

Scheme dependence affects the consistency of one-loop domain wall tension computations.

Abstract

The one-loop tension of the domain wall in the 3+1 dimensional $\phi^4$ double-well model was derived long ago using dimensional regularization. The methods used can only be applied to solitons depending on a single dimension. In the past few months, domain wall tensions have been recalculated using spectral methods with Born subtractions and also linearized soliton perturbation theory, both of which may be generalized to arbitrary solitons. It has been shown that the former agrees with the results of Rebhan et al. In the present work, we argue that, if the same renormalization scheme is chosen, both new results agree.