Non-Abelian duality from vortex moduli: A dual model of color-confinement

Abstract

It is argued that the dual transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G -> H is to be defined by setting the low-energy H system in Higgs phase, so that the dual systern is in confinement phase. The transformation law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v(1) >> v(2)) G (v1)-> H (v2)-> 1, under an unbroken, exact color-flavor diagonal symmetry HC+F similar to (H) over tilde. The transformation property among the regular monopoles characterized by pi(2)(G/H), follows from that among the nonAbelian vortices with flux quantized according to pi, (H), via the isomorphism pi(1)(G) similar to pi(1)(H)/pi(2)(G/H). Our idea is tested against the concrete model s-softly-broken N = 2 supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v(1) >> v(2) >> Lambda) of these models are consistent with those inferred from the fully quantum- mechanical low-energy effective action of the systems (at v(1 center dot) v(2) similar to Lambda). (c) 2007 Elsevier B.V. All rights reserved

Non-Abelian vortices in SO(N) and USp(N) gauge theories

“…GNOW) dualities. Our results in this paper represent further steps along the line of the work [16,26], even though here we have limited ourselves just to several examples and a few general observations. A more systematic discussion on this problem will be presented elsewhere [51].…”

“…[9]- [12] in order to exhaust all possible moduli. The moduli and transformation properties of the moduli in the cases of composite vortices (higherwinding vortices) [13][14][15][16] and semi-local vortices [17,18], have been studied. A new type of (Seiberg-like) duality was found among pairs of models having related vortex moduli, sharing a common sigma-model-lump limit [18].…”

Non-Abelian vortices with an Aharonov-Bohm effect

“…The coupled differential equations (3.12) define the solution only after a specific set of boundary conditions are imposed. The appropriate boundary conditions at large r are 15) so that the squark fields approach the form,…”

New Results on Non-Abelian Vortices — Further Insights Into Monopole, Vortex and Confinement

“…This process endows the monopoles with fully quantum-mechanical non-Abelian (GNO-dual) charges, as has been suggested by the author and others in several occasions [16], but we shall not dwell on this subject further here.…”

“…As transformation groups of fields H andH are relatively non-local, the sought-for transformations of monopoles must look as non-local field transformations from the point of view of the original theory [16]. But the most significant fact is that fully quantum mechanical monopoles appears in the low-energy dual description of a wide class of N = 2 supersymmetric QCD [5,6].…”