Derivative Expansion and Soliton Masses

TL;DR

This paper introduces a simple algorithm for the generalized derivative expansion and applies it to compute one-loop mass corrections for solitons, revealing that supersymmetric models' mass corrections depend only on asymptotic fermionic potentials.

Contribution

It presents a new, straightforward algorithm for the generalized derivative expansion and demonstrates its application to soliton mass corrections in supersymmetric models.

Findings

The algorithm effectively computes one-loop mass corrections.

Total mass correction in N=1 supersymmetric solitons is determined by asymptotic fermionic potentials.

The computed correction matches phase-shift method results, confirming validity.

Abstract

We present a simple algorithm to implement the generalized derivative expansion introduced previously by L-H. Chan, and apply it to the calculation of the one-loop mass correction to the classical soliton mass in the 1+1 dimensional Jacobi model. We then show how this derivative expansion approach implies that the total (bosonic plus fermionic) mass correction in an N=1 supersymmetric soliton model is determined solely by the asymptotic values (and derivatives) of the fermionic background potential. For a static soliton the total mass correction is $-m/(2\pi)$, in agreement with recent analyses using phase-shift methods.