Non-Abelian strings in N=1 supersymmetric QCD

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 nonAbelian 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 N f = 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 but its scale is exponentially small as compared to the scale of the four dimensional bulk theory in contrast to the N = 2 case where these scales are equal. 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 also discuss what happens to confined monopoles at large µ.

Dynamics of non-Abelian strings in the theory interpolating from N=2 to N=1 supersymmetric QCD

“…This model appears as a world sheet theory on a non-Abelian string in N = 2 SQCD deformed by the adjoint field mass µ. It was derived in [16] in two cases, for small and large values of the deformation µ. Here and throughout this paper we will take the mass parameters to lie on the circle (1.3), and we also assume that the deformation parameter is real and positive, µ > 0.…”

“…The first effect derived in [16] is that n i fields entering the N = (2, 2) CP(N − 1) model (1.7) develop an additional potential upon µ deformation which depends on mass differences. This potential in the small µ limit was first found in [29].…”

“…A lot of work has been done to generalize the construction of non-Abelian strings to QCD-like theories with less supersymmetry, in particular to N = 1 SQCD [13,14,15,16] see [7] for a review. One promising approach is to deform N = 2 SQCD by the mass µ of the adjoint matter (µ-deformed SQCD) and study what happen to non-Abelian strings upon this deformation.…”

“…In Ref. [16] the world sheet theory living on the non-Abelian string in the µ-deformed SQCD was found and it was shown that it flows to the non-supersymmetric CP(N −1) model in the limit of large µ.…”

“…First, we will briefly review the non-supersymmetric and the N = (2, 2) supersymmetric models, which were considered before, see for example [18,20,21,22]. After that, we will introduce the model that we will be working with, namely the µ-deformed CP(N −1) model which is an effective theory living on the world sheet of non-Abelian string in µ-deformed SQCD [16].…”