Heterotic flux tubes inN=2supersymmetric QCD withN=1preserving deformations

Abstract

We consider non-Abelian Bogomol'nyi-Prasad-Sommerfield-saturated flux tubes (strings) in $\mathcal{N}=2$ supersymmetric QCD deformed by superpotential terms of a special type breaking $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$. Previously it was believed that world sheet supersymmetry is accidentally enhanced due to the facts that $\mathcal{N}=(1,1)$ supersymmetry is automatically elevated up to $\mathcal{N}=(2,2)$ on $CP(N\ensuremath{-}1)$ and, at the same time, there are no $\mathcal{N}=(0,2)$ generalizations of the bosonic $CP(N\ensuremath{-}1)$ model. Edalati and Tong noted that the target space is in fact $CP(N\ensuremath{-}1)\ifmmode\times\else\texttimes\fi{}C$ rather than $CP(N\ensuremath{-}1)$. This allowed them to suggest a heterotic $\mathcal{N}=(0,2)$ sigma model, with the $CP(N\ensuremath{-}1)$ target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the $\mathcal{N}=(2,2)$ $CP(N\ensuremath{-}1)$ model. We derive the heterotic $\mathcal{N}=(0,2)$ world sheet model directly from the bulk theory. The relation between the bulk and world sheet 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 world sheet 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.