Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model

TL;DR

This paper solves the heterotic N=(0,2) CP(N-1) model in the large-N limit, revealing spontaneous supersymmetry breaking, multiple vacua, and a deconfinement phase, thus advancing understanding of non-Abelian strings in supersymmetric QCD.

Contribution

It provides the first large-N analytical solution of the heterotic N=(0,2) CP(N-1) model, showing spontaneous SUSY breaking and vacuum structure in this context.

Findings

Spontaneous supersymmetry breaking for all deformation parameters

Identification of the Goldstino field in the model

The model exhibits N degenerate vacua with broken Z_{2N} symmetry

Abstract

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the CP(N-1) model with an extra right-handed fermion field and N=(0,2) supersymmetry. This model emerges as a low-energy theory on the worldsheet of the BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by a superpotential of a special type breaking N=2 supersymmetry down to N=1. Using large-N expansion we solve this model to the leading order in 1/N. Our solution exhibits spontaneous supersymmetry breaking for all values of the deformation parameter. We identify the Goldstino field. The discrete Z_{2N} symmetry is shown to be spontaneously broken down to Z_2; therefore, the worldsheet model has N strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic CP(N-1) model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the N=(2,2) CP(N-1) model which has N degenerate vacua with unbroken supersymmetry, and, on the other hand, with nonsupersymmetric CP(N-1) model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic CP(N-1) model in the large-N limit.