Vacuum Structures of Supersymmetric Noncompact Gauge Theory

TL;DR

This paper explores vacuum structures in supersymmetric models with noncompact SU(1,1) symmetry, demonstrating conditions for consistency and symmetry breaking in both global and local frameworks.

Contribution

It introduces a novel approach to noncompact supersymmetric gauge theories with linear symmetry realization and analyzes their vacuum structures.

Findings

The model with two fundamental representations is consistent globally.

The model with one adjoint representation is consistent globally and locally.

Spontaneous symmetry breaking is necessary for model consistency.

Abstract

We consider models with a noncompact symmetry in the framework of $\mathcal{N}=1$ supersymmetry. Contrary to the conventional approach, the noncompact symmetry is realized linearly on all fields without constraints. The models are constructed using noncanonical K\"ahler function and gauge kinetic function, which is introduced for the local case. It is explained that the symmetry needs to be spontaneously broken for the consistency of a model. We study the vacuum structures of two models with the noncompact symmetry SU(1,1) for both global and local cases. One of them includes two fundamental representations of the group and the other includes one adjoint representation. It is shown that the former is consistent for the global case and the latter is consistent for both the global and local cases.