Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction

Abstract

The non-Abelian Josephson junction is a junction of non-Abelian color superconductors sandwiching an insulator, or a non-Abelian domain wall if flexible, whose low-energy dynamics is described by a U(N) principal chiral model with the conventional pion mass. A non-Abelian Josephson vortex is a non-Abelian vortex (color magnetic flux tube) residing inside the junction, that is described as a non-Abelian sine-Gordon soliton. In this paper, we propose Josephson instantons and Josephson monopoles, that is, Yang-Mills instantons and monopoles inside a non-Abelian Josephson junction, respectively, and show that they are described as SU(N) Skyrmions and U(1)N−1 vortices in the U(N) principal chiral model without and with a twisted-mass term, respectively. Instantons with a twisted boundary condition are reduced (or T-dual) to monopoles, implying that CPN−1 lumps are T-dual to CPN−1 kinks inside a vortex. Here we find SU(N) Skyrmions are T-dual to U(1)N−1 vortices inside a wall. Our configurations suggest a yet another duality between CPN−1 lumps and SU(N) Skyrmions as well as that between CPN−1 kinks and U(1)N−1 vortices, viewed from different host solitons. They also suggest a duality between fractional instantons and bions in the CPN−1 model and those in the SU(N) principal chiral model.

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