Abstract
Non-Abelian flux tubes (strings) are well studied in N = 2 supersymmetric QCD in (3+1) dimensions. In addition to translational zero modes they have also orientational moduli associated with rotations of their fluxes inside a non- Abelian group. The dynamics of the orientational moduli is described by the two dimensional CP(N - 1) model living on the world sheet of the non-Abelian string. In this paper we consider a deformation of N = 2 supersymmetric QCD with the U(N) gauge group and Nf = N quark flavors with a mass term μ of the adjoint matter. In the limit of large μ the theory flows to an N = 1 supersymmetric QCD. We study the solution for the non-Abelian string in this limit and derive an effective theory on the string world sheet. The bosonic sector of this theory is still given by the CP(N -1) model. We study also the fermionic sector of the world sheet theory. Upon the deformation the non-Abelian string is no longer BPS and we show that the fermionic superorientational zero modes are all lifted. This leaves us with the pure bosonic CP(N-1) model on the string world sheet in the limit of N = 1 QCD. We discuss what happens to confined monopoles at large μ.
Highlights
The mechanism of confinement based on a monopole condensation [2] was shown to work [3, 4] in the monopole vacua of N = 2 supersymmetric QCD
Searchers for non-Abelian generalization of Seiberg-Witten scenario lead to the discovery of non-Abelian strings [9,10,11,12], see [13,14,15,16] for a review. These BPS nonAbelian vortices are formed in N = 2 SU(N)×U(1) QCD when the theory is in the Higgs phase for quarks, and monopoles are confined
Internal dynamics of the orientational moduli is governed by the CP(N − 1) model living on the string world sheet
Summary
Searchers for non-Abelian generalization of Seiberg-Witten scenario lead to the discovery of non-Abelian strings [9,10,11,12], see [13,14,15,16] for a review These BPS nonAbelian vortices are formed in N = 2 SU(N)×U(1) QCD when the theory is in the Higgs phase for quarks, and monopoles are confined. We study solutions for the non-Abelian string profile functions in the large μ limit and derive the effective theory on the string world sheet. We further consider the case with “extra” quark flavors, N f > N In this case non-Abelian “ semilocal” strings are formed in N = 2 QCD. This potential forces the size of a semilocal string to shrink and it transforms into a local string
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