Heterotic non-Abelian string of a finite length

We consider non-Abelian strings in N=2 supersymmetric quantum chromodynamics (QCD) with the U(N) gauge group and Nf=N quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N=2 supersymmetry down to N=1. Dynamics of orientational zero modes on the string world sheet are described then by CP(N-1) model with N=(0,2) supersymmetry. We study the string of a finite length L assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-N approximation. At N= we find a rich phase structure in the (L,u) plane where u is a deformation parameter. At large L and intermediate u we find a phase with broken Z2N symmetry, N vacua and a mass gap. At large values of L and u still larger we have the Z2N-symmetric phase with a single vacuum and massless fermions. In both phases N=(0,2) supersymmetry is spontaneously broken. We also observe a phase with would-be broken SU(N) symmetry at small L (it is broken only for N=). In the latter phase the mass gap vanishes and the vacuum energy is zero in the leading 1/N approximation. We expect that at large but finite N corrections O(1/N) will break N=(0,2) supersymmetry. Simultaneously, the phase transitions will become rapid crossovers. Finally we discuss how the observed rich phase structure matches the N=(2,2) limit in which the world-sheet theory has a single phase with the mass gap independent of L.