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

TL;DR

This paper explores novel non-Abelian topological solitons, such as instantons and monopoles, within a non-Abelian Josephson junction, revealing dualities among various solitonic configurations and their implications in gauge theories.

Contribution

It introduces Josephson instantons and monopoles in a non-Abelian junction and demonstrates their descriptions as Skyrmions and vortices, uncovering new dualities among these solitons.

Findings

Josephson instantons are described as $SU(N)$ Skyrmions.

Josephson monopoles correspond to $U(1)^{N-1}$ vortices.

Identifies dualities between lumps, kinks, and Skyrmions.

Abstract

Non-Abelian Josephson junction is a junction of non-Abelian color superconductors sandwiching an insulator, or 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.