On Effective Superpotentials and Compactification to Three Dimensions

TL;DR

This paper explores how to derive exact superpotentials for 4D N=2 SO/SP supersymmetric gauge theories compactified to three dimensions, using integrable models like the periodic Toda lattice.

Contribution

It introduces a novel method to compute superpotentials via the Lax matrix of the Toda lattice, linking gauge theory vacua with integrable systems.

Findings

Exact superpotentials obtained from integrable models.

Connection established between different SO groups' vacua.

Framework applicable to both SO and SP gauge theories.

Abstract

We study four dimensional N=2 SO/SP supersymmetric gauge theory on R^3\times S^1 deformed by a tree level superpotential. We will show that the exact superpotential can be obtained by making use of the Lax matrix of the corresponding integrable model which is the periodic Toda lattice. The connection between vacua of SO(2N) and SO(2kN-2k+2) can also be seen in this framework. Similar analysis can also be applied for SO(2N+1) and SP(2N).