Field theories with higher-group symmetry from composite currents

Abstract

Higher-form symmetries are associated with transformations that only act on extended objects, not on point particles. Typically, higher-form symmetries live alongside ordinary, point-particle (0-form), symmetries and they can be jointly described in terms of a direct product symmetry group. However, when the actions of 0-form and higher-form symmetries become entangled, a more general mathematical structure is required, related to higher categorical groups. Systems with continuous higher-group symmetry were previously constructed in a top-down manner, descending from quantum field theories with a specific mixed 't Hooft anomaly. I show that higher-group symmetry also naturally emerges from a bottom-up, low-energy perspective, when the physical system at hand contains at least two different given, spontaneously broken symmetries. This leads generically to a hierarchy of emergent higher-form symmetries, corresponding to the Grassmann algebra of topological currents of the theory, with an underlying higher-group structure. Examples of physical systems featuring such higher-group symmetry include superfluid mixtures and variants of axion electrodynamics.

arXiv comment1+39 pages, 2 tables; v2: added a discussion of charged objects of composite symmetries and some extra references, version to appear in JHEP

References in corpus (48)

• Generalized Global Symmetries
• Local BRST cohomology in gauge theories
• On the Foundations of Chiral Perturbation Theory
• Exploring 2-Group Global Symmetries
• Local BRST cohomology in the antifield formalism: I. General theorems
• A symmetry principle for Topological Quantum Order
• On gauging finite subgroups
• On 2-Group Global Symmetries and Their Anomalies
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• An Invitation to Higher Gauge Theory
• Nonrelativistic effective Lagrangians
• An Introduction to Spontaneous Symmetry Breaking
• Generalized global symmetries and dissipative magnetohydrodynamics
• Notes on generalized global symmetries in QFT
• Field Theories With a Vector Global Symmetry
• GLSM's for gerbes (and other toric stacks)
• Effective Lagrangian for Nonrelativistic Systems
• Low-Energy Quantum Effective Action for Relativistic Superfluids
• Asymptotic conservation laws in field theory
• Counting Rules of Nambu-Goldstone Modes
• Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields
• Higher-form symmetries and 3-group in axion electrodynamics
• Goldstone modes and photonization for higher form symmetries
• General Effective Actions
• Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Notes on gauging noneffective group actions
• Magnetohydrodynamics as superfluidity
• Selected Topics in the Large Quantum Number Expansion
• Superfluids as Higher-form Anomalies
• Invariant Effective Actions, Cohomology of Homogeneous Spaces and Anomalies
• One-form superfluids and magnetohydrodynamics
• Effective field theory of magnetohydrodynamics from generalized global symmetries
• Duality for the Non-Specialist
• Revisiting Wess-Zumino-Witten terms
• Counting Nambu-Goldstone modes of higher-form global symmetries
• Higher-form symmetries and spontaneous symmetry breaking
• Effective Lagrangians for quantum many-body systems
• 2-group global symmetries, hydrodynamics and holography
• General anomaly matching by Goldstone bosons
• Gauged Wess-Zumino terms for a general coset space
• Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries
• Chiral soliton lattice in QCD-like theories
• Homological classification of topological terms in sigma models on homogeneous spaces
• Topological mass generation in gapless systems
• Some results on topological currents in field theory

Cited by in corpus (14)

• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Continuous Generalized Symmetries in Three Dimensions
• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
• Lifetimes of (near) eternal false vacua
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Holographic duals of symmetry broken phases
• Effective Field Theory for Spontaneously Broken Symmetry
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Monopole Breaking of Chern-Weil Symmetries
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• Unstable Nambu-Goldstone modes
• Higher-group global symmetry and the bosonic M5 brane
• Higher-form anomalies and state-operator correspondence beyond conformal invariance