Instantons in Four-Fermi Term Broken SUSY with General Potential

TL;DR

This paper develops a method to solve Euclidean equations of motion for a particle in a general potential with four-Fermi terms, revealing topological corrections to the classical action, exemplified by the Sine-Gordon model.

Contribution

It introduces a general approach to incorporate four-Fermi terms into classical solutions and explicitly computes topological corrections in the Sine-Gordon model.

Findings

Classical action depends on fermionic boundary conditions.

Fermionic corrections are topological, depending only on boundary values.

Explicit solution for the Sine-Gordon model with four-Fermi term.

Abstract

It is shown how to solve the Euclidean equations of motion of a point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective coordinates. The corrections to the classical action due to the presence of fermions are of topological nature in the sense that they depend only on the values of the fields at the boundary points $\tau \to \pm \infty$. As an application, the Sine-Gordon model with a four-Fermi term is solved explicitly and the corrections to the classical action are computed.