Fractons, dipole symmetries and curved spacetime

Abstract

We study complex scalar theories with dipole symmetry and uncover a no-go theorem that governs the structure of such theories and which, in particular, reveals that a Gaussian theory with linearly realised dipole symmetry must be Carrollian. The gauging of the dipole symmetry via the Noether procedure gives rise to a scalar gauge field and a spatial symmetric tensor gauge field. We construct a worldline theory of mobile objects that couple gauge invariantly to these gauge fields. We systematically develop the canonical theory of a dynamical symmetric tensor gauge field and arrive at scalar charge gauge theories in both Hamiltonian and Lagrangian formalism. We compute the dispersion relation of the modes of this gauge theory, and we point out an analogy with partially massless gravitons. It is then shown that these fractonic theories couple to Aristotelian geometry, which is a non-Lorentzian geometry characterised by the absence of boost symmetries. We generalise previous results by coupling fracton theories to curved space and time. We demonstrate that complex scalar theories with dipole symmetry can be coupled to general Aristotelian geometries as long as the symmetric tensor gauge field remains a background field. The coupling of the scalar charge gauge theory requires a Lagrange multiplier that restricts the Aristotelian geometries.

78 pages including three appendices; v2: Typos fixed, several improvements to Sec. 7; v3: updated to published version; v4: Fixed more typos, updated refs

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Cited by in corpus (69)

• The dipolar Bose-Hubbard model
• Magic Fermions: Carroll and Flat Bands
• Conformal Carroll Scalars with Boosts
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Carroll/fracton particles and their correspondence
• Carrollian hydrodynamics from symmetries
• Carrollian Origins of Bjorken Flow
• Carroll black holes
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Carroll covariant scalar fields in two dimensions
• Infinite families of fracton fluids with momentum conservation
• Gravity as a gapless phase and biform symmetries
• Boosting to BMS
• Carrollian fluids and spontaneous breaking of boost symmetry
• Generalized Symmetries of the Graviton
• Hydrodynamics of dipole-conserving fluids
• One-Loop Quantum Effects in Carroll Scalars
• Foliated BF theories and Multipole symmetries
• Carrollian Origin of Spacetime Subsystem Symmetry
• Carrollian conformal scalar as flat-space singleton
• A Chern-Simons theory for dipole symmetry
• Heavy-ion collisions, Gubser flow, and Carroll hydrodynamics
• Ideal fracton superfluids
• Quantizing Carrollian field theories
• A symmetry principle for gauge theories with fractons
• Emergent Dipole Gauge Fields and Fractons
• Covariant fracton gauge theory with boundary
• Lifshitz symmetry: Lie algebras, spacetimes and particles
• Carrollian Supersymmetry and SYK-like models
• Symmetric higher rank topological phases on generic graphs
• Carrollian Yang-Mills Theory
• Fracton gravity from spacetime dipole symmetry
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Quantization of Carrollian conformal scalar theories
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• Fracton-elasticity duality on curved manifolds
• Memory Effect and Carroll Symmetry: 50 years later
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Asymptotic symmetries and soft charges of fractons
• Stress tensors of 3d Carroll CFTs
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids
• Quantization of Carrollian fermions
• Quasi-topological fractons: a 3D dipolar gauge theory
• MultiCarroll dynamics
• Fractonic self-duality and covariant magnetic fractons
• A post-Gaussian approach to dipole symmetries and interacting fractons
• Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
• Supersymmetric Carroll Galileons in Three Dimensions
• Hydrodynamics in the Carrollian regime
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Fractons in curved space
• Anisotropic conformal Carroll field theories and their gravity duals
• Planons and their Carroll-Galilei symmetries
• Quadrupole gauge theory: anti-Higgs mechanism and elastic dual
• Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
• Galilei particles revisited
• Possible ambient kinematics
• Scaling Symmetry and Carrollian Gravity
• Free-field construction of Carrollian $W_N$-algebras
• Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant
• The gauging procedure and carrollian gravity
• A complex scalar field theory for charged fluids, superfluids, and fracton fluids
• Collective dynamics in holographic fractonic solids
• Strings near BTZ black holes: A Carrollian Chronicle
• Covariant Fracton Electrodynamics in Six Dimensions
• Rotating Carroll Black Holes: A No Go Theorem
• Emergent fracton strings from covariant bi-form gauge field theory
• A non-lorentzian primer