SUSY gauge theories and Whitham integrable systems from compactification and SUSY breaking

TL;DR

This paper reviews how supersymmetric gauge theories relate to integrable systems, especially through compactification and SUSY breaking, revealing new insights into their effective actions and BPS spectra.

Contribution

It demonstrates the emergence of integrable structures from compactified SUSY gauge theories and connects Whitham systems to uncompactified theories via averaging methods.

Findings

Integrable systems naturally arise from SUSY gauge theories through compactification.

Whitham systems correspond to uncompactified theories and are recovered by averaging.

The formulation links bare and quantum variables with superpotentials in SUSY theories.

Abstract

We review the Seiberg-Witten construction of low-energy effective actions and BPS spectra in SUSY gauge theories and its formulation in terms of integrable systems. It is also demonstrated how this formulation naturally appears from the compactified version of the theory with partially broken supersymmetry so that the integrable structures arise from the relation between bare and quantum variables and superpotentials of SUSY gauge theories. The Whitham integrable systems, literally corresponding to the uncompactified theory, are then restored by averaging over fast variables in the decompactification limit.