Large-N Solution of the Heterotic Weighted Non-Linear Sigma-Model

TL;DR

This paper analyzes a heterotic two-dimensional gauged non-linear sigma-model with a weighted projective space target, solving it in the large-N limit to explore supersymmetry breaking and conformal points relevant to non-Abelian vortices in supersymmetric gauge theories.

Contribution

It provides the first large-N solution of a heterotic weighted non-linear sigma-model and investigates supersymmetry preservation at special mass parameter values.

Findings

Supersymmetry is generally broken in the model.

At specific mass values, a new super-conformal branch appears.

The model captures low-energy physics of non-Abelian semi-local vortices.

Abstract

We study a heterotic two-dimensional N=(0,2) gauged non-linear sigma-model whose target space is a weighted complex projective space. We consider the case with N positively and N^~=N_F - N negatively charged fields. This model is believed to give a description of the low-energy physics of a non-Abelian semi-local vortex in a four-dimensional N=2 supersymmetric U(N) gauge theory with N_F > N matter hypermultiplets. The supersymmetry in the latter theory is broken down to N=1 by a mass term for the adjoint fields. We solve the model in the large-N approximation and explore a two-dimensional subset of the mass parameter space for which a discrete Z_{N-N^~} symmetry is preserved. Supersymmetry is generically broken, but it is preserved for special values of the masses where a new branch opens up and the model becomes super-conformal.