Heat kernels and zeta-function regularization for the mass of the supersymmetric kink

TL;DR

This paper applies zeta-function and heat kernel techniques to compute the quantum mass of supersymmetric kinks, addressing regularization ambiguities and comparing different renormalization methods.

Contribution

It introduces a detailed analysis of zeta-function and heat kernel regularization methods for supersymmetric kinks, clarifying their equivalence and fixing ambiguities through specific renormalization conditions.

Findings

Quantum mass computed using zeta-function regularization.

Heat kernel subtraction methods yield consistent results.

Renormalization conditions ensure physical mass vanishes at infinite mass gap.

Abstract

We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We fix ambiguities by the renormalization condition that the quantum mass vanishes as one lets the mass gap tend to infinity while keeping scattering data fixed. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and apply standard heat kernel subtractions. Finally we discuss to what extent these procedures are equivalent to the usual renormalization conditions that tadpoles vanish.