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 $\mathbb{C}{P}^{N-1}$ lumps are T-dual to $\mathbb{C}{P}^{N-1}$ 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 $\mathbb{C}{P}^{N-1}$ lumps and $SU(N)$ Skyrmions as well as that between $\mathbb{C}{P}^{N-1}$ kinks and $U(1{)}^{N-1}$ vortices, viewed from different host solitons. They also suggest a duality between fractional instantons and bions in the $\mathbb{C}{P}^{N-1}$ model and those in the $SU(N)$ principal chiral model.

• Received 30 March 2015

DOI:https://doi.org/10.1103/PhysRevD.92.045010