Supersymmetry and Solitons: N=2 and N=0

TL;DR

This work develops an algebraic, model-independent framework leveraging supersymmetry to establish bounds and equations for topological solitons and instantons across various dimensions, applicable to both supersymmetric and non-supersymmetric theories.

Contribution

It introduces a novel algebraic approach to derive bounds and equations for solitons and instantons, independent of specific models, using supersymmetry in multiple dimensions.

Findings

Established algebraic, model-independent bounds for solitons and instantons

Unified treatment of supersymmetric and non-supersymmetric theories

Applicable across various spacetime dimensions

Abstract

This talk summarizes our recent work establishing an algebraic, model-independent basis for the existence of \B bounds and \B equations for topologically non-trivial solitons and instantons. Our arguments use supersymmetry in an essential way to understand both supersymmetric and non-supersymmetric theories. Our arguments are constructive and work in nearly any number of dimensions. Presented at and to appear in the proceedings of the XX^{th} International Colloquium on Group Theoretical Methods in Physics, Osaka, July 1994.