2-group global symmetries, hydrodynamics and holography

Abstract

2-group global symmetries are a particular example of how higher-form and conventional global symmetries can fuse together into a larger structure. We construct a theory of hydrodynamics describing the finite-temperature realization of a 2-group global symmetry composed out of $U(1)$ zero-form and $U(1)$ one-form symmetries. We study aspects of the thermodynamics from a Euclidean partition function and derive constitutive relations for ideal hydrodynamics from various points of view. Novel features of the resulting theory include an analogue of the chiral magnetic effect and a chiral sound mode propagating along magnetic field lines. We also discuss a minimalist holographic description of a theory dual to 2-group global symmetry and verify predictions from hydrodynamic descriptions. Along the way we clarify some aspects of symmetry breaking in higher-form theories at finite temperature.

32 pages + appendices, 6 figures

References in corpus (15)

• The Chiral Magnetic Effect
• Generalized Global Symmetries
• Chiral Magnetic Wave
• Higher-Dimensional Algebra V: 2-Groups
• Low-Energy Quantum Effective Action for Relativistic Superfluids
• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• Deconstructing holographic liquids
• The turbulent chiral-magnetic cascade in the early universe
• Higher-form symmetries and 3-group in axion electrodynamics
• 2-Group Symmetries of 6d Little String Theories and T-duality
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Wess-Zumino Terms for Relativistic Fluids, Superfluids, Solids, and Supersolids
• A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems
• Dissipative String Fluids
• From Maxwell-Chern-Simons theory in $Ad{S}_3$ towards hydrodynamics in 1+1 dimensions

Cited by in corpus (13)

• The Branes Behind Generalized Symmetry Operators
• 2-Group Symmetries in Class S
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Lifetimes of (near) eternal false vacua
• Anomalies of Generalized Symmetries from Solitonic Defects
• Field theories with higher-group symmetry from composite currents
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• Higher-group global symmetry and the bosonic M5 brane
• WZW terms without anomalies: generalised symmetries in chiral Lagrangians
• Effective field theories of dissipative fluids with one-form symmetries
• Scheme dependence and instability of double-trace deformations for gauge fields in AdS${}_5$