Moduli Space Potentials for Heterotic non-Abelian Flux Tubes: Weak Deformation

TL;DR

This paper studies non-Abelian flux tubes in N=2 supersymmetric QCD with a deformation that breaks supersymmetry to N=1, calculating their tensions and effective world-sheet theories, revealing quantum effects correspondence.

Contribution

It derives the deformation potential for heterotic CP(N_f-1) models on the string world sheet, expanding the class of known heterotically deformed models and linking bulk quantum effects to world-sheet dynamics.

Findings

Classical and quantum string tensions calculated.

Deformation potential on the world sheet derived.

Quantum effects in bulk and world-sheet theories are exactly matched.

Abstract

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N_f flavors of massive quarks deformed by the mass term \mu for the adjoint matter, W=\mu A^2, assuming that N\leq N_f<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small \mu, so that the Z_N strings preserve, in a sense, their BPS nature. We calculate string tensions both in the classical and quantum regimes. Then we translate our results for the tensions in terms of the effective low-energy weighted CP(N_f-1) model on the string world sheet. The bulk \mu-deformation makes this theory N= (0,2) supersymmetric heterotic weighted CP(N_f-1) model in two dimensions. We find the deformation potential on the world sheet. This significantly expands the class of the heterotically deformed CP models emerging on the string world sheet compared to that suggested by Edalati and Tong. Among other things, we show that nonperturbative quantum effects in the bulk theory are exactly reproduced by the quantum effects in the world-sheet theory.