Effective gauge theories of superfluidity with topological order

Abstract

We discuss the low-energy dynamics of superfluidity with topological order in $(3+1)$ spacetime dimensions. We generalize a topological $BF$ theory by introducing a non-square $K$ matrix, and this generalized $BF$ theory can describe massless Nambu-Goldstone bosons and anyonic statistics between vortices and quasiparticles. We discuss the general structure of discrete and continuous higher-form symmetries in this theory, which can be used to classify quantum phases. We describe how to identify the appearance of topological order in such systems and discuss its relation to a mixed 't Hooft anomaly between discrete higher-form symmetries. We apply this framework to the color-flavor locked phase of dense QCD, which shows anyonic particle-vortex statistics while no topological order appears. An explicit example of superfluidity with topological order is discussed.

34 pages, no figure; v2: added discussions and Appendix D

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• Generalized Global Symmetries
• Color superconductivity in dense quark matter
• Symmetries and Strings in Field Theory and Gravity
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Anomaly matching in QCD thermal phase transition
• Topological Interactions of Non-Abelian Vortices with Quasi-Particles in High Density QCD

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