Supersymmetric Nonlinear Sigma Models as Gauge Theories

TL;DR

This paper demonstrates how supersymmetric nonlinear sigma models can be formulated as gauge theories, especially for hermitian symmetric spaces, by imposing constraints and utilizing auxiliary superfields to control the target manifold's compactness.

Contribution

It provides a gauge theory formulation for all supersymmetric nonlinear sigma models with hermitian symmetric space target manifolds, clarifying the role of auxiliary superfields and gauge symmetries.

Findings

Target manifolds are non-compact without D-term constraints.

Gauge symmetries eliminate non-compact directions, making the manifold compact.

All hermitian symmetric space sigma models can be formulated as gauge theories.

Abstract

Supersymmetric nonlinear sigma models are obtained from linear sigma models by imposing supersymmetric constraints. If we introduce auxiliary chiral and vector superfields, these constraints can be expressed by D-terms and F-terms depending on the target manifolds. Auxiliary vector superfields appear as gauge fields without kinetic terms. If there are no D-term constraints, the target manifolds are always non-compact manifolds. When all the degrees of freedom in these non-compact directions are eliminated by gauge symmetries, the target manifold becomes compact. All supersymmetric nonlinear sigma models, whose target manifolds are the hermitian symmetric spaces, are successfully formulated as gauge theories.