The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory

TL;DR

This paper determines the phase structure of a mass-deformed SU(2)xSU(2) N=2 supersymmetric theory compactified on a circle, revealing its vacua and condensates through integrable system techniques.

Contribution

It provides an exact analysis of the phase structure and vacua of the mass-deformed SU(2)xSU(2) theory using integrable systems and superpotential methods.

Findings

Identifies four confining vacua, two Higgs vacua, and two massless Coulomb vacua.

Calculates all scalar condensates in each vacuum.

Matches vacuum structure with tree-level superpotential analysis.

Abstract

The phase structure of the finite SU(2)xSU(2) theory with N=2 supersymmetry, broken to N=1 by mass terms for the adjoint-valued chiral multiplets, is determined exactly by compactifying the theory on a circle of finite radius. The exact low-energy superpotential is constructed by identifying it as a linear combination of the Hamiltonians of a certain symplectic reduction of the spin generalized elliptic Calogero-Moser integrable system. It is shown that the theory has four confining, two Higgs and two massless Coulomb vacua which agrees with a simple analysis of the tree-level superpotential of the four-dimensional theory. In each vacuum, we calculate all the condensates of the adjoint-valued scalars.