Abstract
We define a nonabelian particle–vortex duality as a 3-dimensional analogue of the usual 2-dimensional worldsheet nonabelian T-duality. The transformation is defined in the presence of a global SU(2) symmetry and, although derived from a string theoretic setting, we formulate it generally. We then apply it to so-called “semilocal strings” in an SU(2)G×U(1)L gauge theory, originally discovered in the context of cosmic string physics.
Highlights
Beginning with the remarkable correspondence between the sine-Gordon and massive Thirring models [1], dualities have played a crucial role in the modern understanding of quantum field theories
In [5], this duality was defined as a path integral transformation in a manifestly symmetric way, and embedded into a planar N = 6 Chern–Simons-matter theory commonly known as the ABJM model, which is itself known to be dual to the type IIA superstring on an AdS4 × CP3 background [6]
Μνρ ∂ν jρ Abelian particle–vortex duality has proven a powerful tool in the understanding of bosonic systems that range from anyonic superconductivity through to cosmic strings
Summary
Beginning with the remarkable correspondence between the sine-Gordon and massive Thirring models [1], dualities have played a crucial role in the modern understanding of quantum field theories. One possible reason for the dearth of literature on the subject could be that its utility lies primarily in condensed matter systems which, being usually non-relativistic are much less susceptible to the powerful relativistic methods employed in high energy theory Another is likely the fact that the duality was generally less well-defined than its (3 + 1)-dimensional counterpart. By generalizing the procedure to (2 + 1)-dimensions, we obtain a non-abelian version of particle–vortex duality that acts on gauge theories with a global SU(2), as well as a local symmetry Recognizing that this is precisely the set-up for the “semi-local” vortices found in [14] (see [15,16]) in the context of cosmic strings in the case of a local U (1) symmetry, we explicitly exhibit the action of the nonabelian particle–vortex transformation on these solutions. This article should be viewed as a proof-of-principle of a phenomenon with potential application from condensed matter to cosmology, with a longer companion paper to follow in which we will elaborate further on the duality and provide more substantial examples [17]
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