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

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.

30 pages, 6 figures, v3: published version

References in corpus (36)

• Color superconductivity in dense quark matter
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Instantons in the Higgs Phase
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Universal Reconnection of Non-Abelian Cosmic Strings
• On the moduli space of semilocal strings and lumps
• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• D-brane Construction for Non-Abelian Walls
• Skyrmions from Instantons inside Domain Walls
• Josephson vortices and the Atiyah-Manton construction
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Instanton constituents in the O(3) model at finite temperature
• Matryoshka Skyrmions
• Domain wall Skyrmions
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Global Structure of Moduli Space for BPS Walls
• Incarnations of Skyrmions
• Domain Walls with Non-Abelian Clouds
• Statistical Mechanics of Vortices from D-branes and T-duality
• Intersecting Solitons, Amoeba and Tropical Geometry
• Non-Abelian Sine-Gordon Solitons
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Confined Magnetic Monopoles in Dense QCD
• Non-Abelian Monopoles in the Higgs Phase
• Chains of Skyrmions
• Localization of Gauge Fields and Monopole Tunnelling
• Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices
• Neutral bions in the CP^{N-1} model for resurgence
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Effective field theories on solitons of generic shapes
• Instantons confined by monopole strings

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• Non-Abelian Sine-Gordon Solitons
• Relations among topological solitons
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• Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices
• Chiral Magnets from String Theory
• Topological Defects in the Georgi-Machacek Model
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Field theoretical model of multi-layered Josephson junction and dynamics of Josephson vortices
• Chemical bonds of two vortex species with a generalized Josephson term and arbitrary charges
• Strings and skyrmions on domain walls
• BPS pion domain walls in the supersymmetric chiral Lagrangian
• Chiral non-Abelian vortex molecules in dense QCD
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Chiral non-Abelian domain walls in the Ginzburg-Landau theory