NonAbelian vortices, large winding limits and Aharonov-Bohm effects

Abstract

Remarkable simplification arises from considering vortex equations in the large winding limit. This was recently used [1] to display all sorts of vortex zeromodes, the orientational, translational, fermionic as well as semi-local, and to relate them to the apparently distinct phenomena of the Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to more general types of BPS nonAbelian vortices, taking as a prototype a system with gauged U 0 (1) × SU ℓ (N ) × SU r (N ) symmetry where the VEV of charged scalar fields in the bifundamental representation breaks the symmetry to SU(N ) ℓ+r . The presence of the massless SU(N ) ℓ+r gauge fields in 4D bulk introduces all sorts of nonlocal, topological phenomena such as the nonAbelian Aharonov-Bohm effects, which in the theory with global SU r (N ) group (g r = 0) are washed away by the strongly fluctuating orientational zeromodes in the worldsheet. Physics changes qualitatively at the moment the right gauge coupling constant g r is turned on.

Geometry and dynamics of a coupled 4D-2D quantum field theory

“…i.e., 32) where the rotation matrix That the vortex (internal) moduli space is exactly a CP N −1 in our model has been verified recently in [16,17] by studying these vortex solutions in the large-winding limit, where vortex configurations can be analytically determined, and accordingly all zero modes can be determined by following the analysisà la Nielsen-Olesen-Ambjorn [19]- [21].…”

“…}, various closed paths encircling these vortices give rise to nonAbelian AB effects: the gauge transformations experienced by a particle depend on the order in which various vortices are circumnavigated. These and many other beautiful features related to such systems have been discussed in [12,13,16,17].…”

“…Even in the case of vortices with constant {B i }, the relative orientations of multiple vortex systems do have observable effects and hence are physical [12,13,16,17]. Consider two or more parallel vortices with different orientations, {B i }.…”

Index theorem for non-supersymmetric fermions coupled to a non-Abelian string and electric charge quantization

“…The Lorentz indices in (12) are contracted as ψη ≡ ε αβ ψ α η β and so on, according to the standard four-dimensional rule. Obviously, the expectation value (7) generates mass terms to all quark fields introduced above.…”

Aharonov-Bohm defects

“…It was also suggested that AB cosmic strings may give a possible observational evidence of string theory [7,8]. Non-Abelian vortices in supersymmetric gauge theory [9][10][11][12][13][14][15][16][17][18][19][20][21] exhibit AB effects [22][23][24] including non-Abelian generalization of AB effects [25], once a part of flavor symmetry is gauged [26]. In dense QCD which may be relevant for cores of neutron stars, a color magnetic flux tube in the 2SC phase exhibits AB effects for quarks [27], while a non-Abelian vortex (color magnetic flux tube) in the color-flavor locked phase [28][29][30][31][32][33] also exhibits (electromagnetic) AB effects for charged particles [34] as well as Z 3 (color) AB effects for quarks [35][36][37][38].…”