Once more on the BPS bound for the susy kink

TL;DR

This paper introduces a new regularization scheme for calculating one-loop quantum corrections to the mass and central charge of the susy kink, ensuring the BPS bound is saturated and aligning with previous results.

Contribution

It proposes a novel momentum cut-off scheme with an interpolating function and a new regularization method for the central charge, improving the consistency of quantum corrections in susy kink models.

Findings

The new scheme reproduces known results for the quantum mass and central charge.

It confirms the saturation of the BPS bound at one-loop level.

Mode number regularization yields consistent results when applied to kink-antikink systems.

Abstract

We consider a new momentum cut-off scheme for sums over zero-point energies, containing an arbitrary function f(k) which interpolates smoothly between the zero-point energies of the modes around the kink and those in flat space. A term proportional to df(k)/dk modifies the result for the one-loop quantum mass M^(1) as obtained from naive momentum cut-off regularization, which now agrees with previous results, both for the nonsusy and susy case. We also introduce a new regularization scheme for the evaluation of the one-loop correction to the central charge Z^(1), with a cut-off K for the Dirac delta function in the canonical commutation relations and a cut-off \Lambda for the loop momentum. The result for Z^(1) depends only on whether K>\Lambda or K<\Lambda or K=\Lambda. The last case yields the correct result and saturates the BPS bound, M^(1)=Z^(1),in agreement with the fact that multiplet shortening does occur in this N=(1,1) system. We show how to apply mode number regularization by considering first a kink-antikink system, and also obtain the correct result with this method. Finally we discuss the relation of these new schemes to previous approaches based on the Born expansion of phase shifts and higher-derivative regularization.