Vacua of Massive Hyper-Kahler Sigma Models with Non-Abelian Quotient

TL;DR

This paper constructs massive hyper-Kahler sigma models with non-Abelian quotients, revealing discrete vacua for U(M) quotients and none for SU(M), advancing understanding of supersymmetric gauge theory vacua.

Contribution

It introduces non-toric massive hyper-Kahler sigma models with non-Abelian quotients in superfield formalisms, detailing their vacuum structures.

Findings

U(M) quotient yields N!/[M! (N-M)!] discrete vacua

SU(M) quotient results in no discrete vacua

Models are constructed in N=1 superfield and harmonic superspace formalisms

Abstract

The Higgs branch of N=2 supersymmetric gauge theories with non-Abelian gauge groups are described by hyper-Kahler (HK) nonlinear sigma models with potential terms. With the non-Abelian HK quotient by U(M) and SU(M) gauge groups, we give the massive HK sigma models that are not toric in the N=1 superfield formalism and the harmonic superspace formalism. The U(M) quotient gives N!/[M! (N-M)!] discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua.