Large-Nsolution of the heteroticN=(0,2)two-dimensionalCP(N−1)model

Abstract

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the $CP(N\ensuremath{-}1)$ model with an extra right-handed fermion field and $\mathcal{N}=(0,2)$ supersymmetry. This model emerges as a low-energy theory on the world sheet of the Bogomol'nyi-Prasad-Sommerfield-saturated flux tubes (strings) in $\mathcal{N}=2$ supersymmetric QCD deformed by a superpotential of a special type breaking $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$. 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 world sheet model has $N$ strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic $CP(N\ensuremath{-}1)$ model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the $\mathcal{N}=(2,2)$ $CP(N\ensuremath{-}1)$ model which has $N$ degenerate vacua with unbroken supersymmetry, and, on the other hand, with the nonsupersymmetric $CP(N\ensuremath{-}1)$ model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic $CP(N\ensuremath{-}1)$ model in the large-$N$ limit.