Abstract
Abstract The interplay of gauge dynamics and flavor symmetries often leads to remarkably subtle phenomena in the presence of soliton configurations. Non-Abelian vortices — vortex solutions with continuous internal orientational moduli — provide an example. Here we study the effect of weakly gauging a U(1) R subgroup of the flavor symmetry on such BPS vortex solutions. Our prototypical setting consists of an SU(2) × U(1) gauge theory with N f = 2 sets of fundamental scalars that break the gauge symmetry to an “electromagnetic” U(1). The weak U(1) R gauging converts the well-known CP 1 orientation modulus |B| of the non-Abelian vortex into a parameter characterizing the strength of the magnetic field that is responsible for the Aharonov-Bohm effect. As the phase of B remains a genuine zero mode while the electromagnetic gauge symmetry is Higgsed in the interior of the vortex, these solutions are superconducting strings.
Highlights
Appropriate 2D sigma model that has its own nontrivial, large-distance, quantum dynamics
We restricted ourselves in this paper to the simplest non-trivial prototype model based on SU(2)L × U0(1) × U(1)R gauge symmetry for the sake of clarity of presentation, it is quite straightforward and rather interesting, to extend our analysis to more general gauge groups and patterns of partial weak gauging
Even though our derivation and the persistence of the vortex moduli space upon U(1)R gauging both depend on the BPS nature of the model considered, the occurrence of the “electromagnetic” AB effect itself has a clear physical explanation, and is independent of the BPS approximation
Summary
Before introducing the weak gauging of a part of the flavor symmetry, let us first briefly review a few salient features of the non-Abelian vortex. U(1) gauge theory with two scalar fields transforming in the fundamental representation, Q = q1 q2 , written in a color-flavor mixed 2 × 2 matrix form. An individual vortex solution breaks the SU(2)C+F global symmetry to a U(1) subgroup and so it develops an orientational modulus B ∈ CP1 = SU(2)/U(1). The vortex solution with a generic orientation and in the regular gauge takes the form. Perturbations of these solutions can be described by promoting the modulus B to a collective coordinate which depends upon the worldsheet coordinates of the vortex. Our main interest below is to determine the fate of these CP1 collective coordinates in the presence of an external, weak U(1)R gauge field
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