Heterotic Flux Tubes in N=2 SQCD with N=1 Preserving Deformations

TL;DR

This paper derives a heterotic N=(0,2) sigma model from deformed N=2 SQCD, revealing supersymmetry breaking and complex relations between bulk and worldsheet parameters, advancing understanding of flux tubes in supersymmetric theories.

Contribution

It provides a direct derivation of the heterotic N=(0,2) worldsheet model from bulk theory and analyzes supersymmetry breaking in deformed N=2 SQCD.

Findings

Derived the heterotic N=(0,2) model from bulk theory.

Found supersymmetry is spontaneously broken at small deformations.

Established a geometric representation for the heterotic model.

Abstract

We consider non-Abelian BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Previously it was believed that worldsheet supersymmetry is "accidentally" enhanced due to the facts that N =(1,1) SUSY is automatically elevated up to N=(2,2) on CP(N-1) and, at the same time, there are no N=(0,2) generalizations of the bosonic CP(N-1) model. Edalati and Tong noted that the target space is in fact CP(N-1) x C rather than CP(N-1). This allowed them to suggest a "heterotic" N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) worldsheet model directly from the bulk theory. The relation between the bulk and worldsheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the worldsheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.