Spontaneously Broken Boosts in CFTs

Abstract

Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as $O(1)$. We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.

arXiv comment50+13 pages,4 figures; matches the published version

References in corpus (42)

• Renormalization Group Approach to Interacting Fermions
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Conformal Four Point Functions and the Operator Product Expansion
• Eigenstate Thermalization Hypothesis
• Conformal Partial Waves and the Operator Product Expansion
• The Analytic Bootstrap and AdS Superhorizon Locality
• Spinning Conformal Correlators
• Lectures on hydrodynamic fluctuations in relativistic theories
• Convexity and Liberation at Large Spin
• Spinning Conformal Blocks
• The Constraints of Conformal Symmetry on RG Flows
• Operator bases, $S$-matrices, and their partition functions
• Entanglement Entropy, Trace Anomalies and Holography
• The Effective Theory of Long Strings
• Semiclassics, Goldstone Bosons and CFT data
• A Constraint on Defect and Boundary Renormalization Group Flows
• Effective String Theory Revisited
• Universal Entanglement and Boundary Geometry in Conformal Field Theory
• Conformal Bootstrap At Large Charge
• Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature
• A limit for large $R$-charge correlators in $\mathcal{N}=2$ theories
• Displacement Operators and Constraints on Boundary Central Charges
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• Weyl anomaly for Wilson surfaces
• Boundary terms of conformal anomaly
• The local Callan-Symanzik equation: structure and applications
• Heavy Operators and Hydrodynamic Tails
• Vector Models in the Singlet Sector at Finite Temperature
• Universal correlation functions in rank 1 SCFTs
• Operator Dimensions from Moduli
• Extremal Correlators and Random Matrix Theory
• Defect $a$-Theorem and $a$-Maximization
• Rotating superfluids and spinning charged operators in conformal field theory
• $\mathcal{N}=2$ conformal gauge theories at large R-charge: the $SU(N)$ case
• Spontaneously broken boosts and the Goldstone continuum
• Quantum thermalization and Virasoro symmetry
• EFT Asymptotics: the Growth of Operator Degeneracy
• Symmetry Obstruction to Fermi Liquid Behavior in the Unitary Limit
• Large Charge Sector of 3d Parity-Violating CFTs
• Transition of Large $R$-Charge Operators on a Conformal Manifold
• Symmetry Realization via a Dynamical Inverse Higgs Mechanism
• Superfluids, vortices and spinning charged operators in 4d CFT

Cited by in corpus (10)

• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Spin Impurities, Wilson Lines and Semiclassics
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Giant Vortices and the Regge Limit
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Inflationary Adler Conditions
• Evidence for 3d bosonization from monopole operators
• D-branes and Orbit Average
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture