Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD

TL;DR

This paper studies non-Abelian semilocal strings in N=2 supersymmetric QCD, deriving their effective world-sheet theory and analyzing quantum effects, revealing conditions for their stability and implications for confinement.

Contribution

It provides a direct field-theoretic derivation of the world-sheet theory for semilocal non-Abelian strings and confirms the Hanany-Tong conjecture in a specific supersymmetric context.

Findings

Derived explicit world-sheet theory for semilocal non-Abelian strings.

Confirmed the Hanany-Tong conjecture in the semiclassical limit.

Showed that quantum effects do not lift the Higgs branch, preventing confinement.

Abstract

We consider a benchmark bulk theory in four-dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N_f flavors of fundamental matter hypermultiplets (quarks). The nature of the BPS strings in this benchmark theory crucially depends on N_f. If N_f\geq N and all quark masses are equal, it supports non-Abelian BPS strings which have internal (orientational) moduli. If N_f>N these strings become semilocal, developing additional moduli \rho related to (unlimited) variations of their transverse size. Using the U(2) gauge group with N_f=3,4 as an example, we derive an effective low-energy theory on the (two-dimensional) string world sheet. Our derivation is field-theoretic, direct and explicit: we first analyze the Bogomol'nyi equations for string-geometry solitons, suggest an ansatz and solve it at large \rho. Then we use this solution to obtain the world-sheet theory. In the semiclassical limit our result confirms the Hanany-Tong conjecture, which rests on brane-based arguments, that the world-sheet theory is N=2 supersymmetric U(1) gauge theory with N positively and N_e=N_f-N negatively charged matter multiplets and the Fayet-Iliopoulos term determined by the four-dimensional coupling constant. We conclude that the Higgs branch of this model is not lifted by quantum effects. As a result, such strings cannot confine. Our analysis of infrared effects, not seen in the Hanany-Tong consideration, shows that, in fact, the derivative expansion can make sense only provided the theory under consideration is regularized in the infrared, e.g. by the quark mass differences. The world-sheet action discussed in this paper becomes a bona fide low-energy effective action only if \Delta m_{AB}\neq 0.