Conformal Bootstrap At Large Charge

Abstract

We consider unitary CFTs with continuous global symmetries in $d>2$. We consider a state created by the lightest operator of large charge $Q\gg 1$ and analyze the correlator of two light charged operators in this state. We assume that the correlator admits a well-defined large $Q$ expansion and, relatedly, that the macroscopic (thermodynamic) limit of the correlator exists. We find that the crossing equations admit a consistent truncation, where only a finite number $N$ of Regge trajectories contribute to the correlator at leading nontrivial order. We classify all such truncated solutions to the crossing. For one Regge trajectory $N=1$, the solution is unique and given by the effective field theory of a Goldstone mode. For two or more Regge trajectories $N\ge 2$, the solutions are encoded in roots of a certain degree $N$ polynomial. Some of the solutions admit a simple weakly coupled EFT description, whereas others do not. In the weakly coupled case, each Regge trajectory corresponds to a field in the effective Lagrangian.

50 pages, 1 figure

References in corpus (25)

• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Critical Phenomena and Renormalization-Group Theory
• The String Landscape, Black Holes and Gravity as the Weakest Force
• Holography from Conformal Field Theory
• Conformal Partial Waves and the Operator Product Expansion
• The Analytic Bootstrap and AdS Superhorizon Locality
• Spinning Conformal Correlators
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Spinning Conformal Blocks
• OPE Convergence in Conformal Field Theory
• Holographic quantum matter
• Conformal Partial Waves: Further Mathematical Results
• Semiclassics, Goldstone Bosons and CFT data
• Compensating strong coupling with large charge
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Conformal dimensions via large charge expansion
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• Operator Dimensions from Moduli
• Partition function on spheres: how (not) to use zeta function regularization
• Matrix models at large charge

Cited by in corpus (57)

• The statistical mechanics of near-extremal black holes
• The Conformal Bootstrap at Finite Temperature
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Universality at large transverse spin in defect CFT
• Selected Topics in the Large Quantum Number Expansion
• Analytic Euclidean Bootstrap
• Heavy Operators and Hydrodynamic Tails
• Universal correlation functions in rank 1 SCFTs
• Holographic thermal correlators from supersymmetric instantons
• Spin Impurities, Wilson Lines and Semiclassics
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Black Holes, Heavy States, Phase Shift and Anomalous Dimensions
• On the large R-charge $\mathcal{N}=2$ chiral correlators and the Toda equation
• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• Delayed Deconfinement and the Hawking-Page Transition
• Gravitational orbits, double-twist mirage, and many-body scars
• Extremal Correlators and Random Matrix Theory
• Scalar CFTs and Their Large N Limits
• Universal Asymptotics for High Energy CFT Data
• Black Holes and Conformal Regge Bootstrap
• A note on the large charge expansion in 4d CFT
• Spontaneously Broken Boosts in CFTs
• An AdS/EFT correspondence at large charge
• The large charge expansion at large N
• Giant Vortices and the Regge Limit
• Generating functions and large-charge expansion of integrated correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Charging the Conformal Window
• More on the Weak Gravity Conjecture via Convexity of Charged Operators
• The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals
• The large-charge expansion for Schrödinger systems
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• The OPE meets semiclassics
• The statistical mechanics of near-BPS black holes
• Large Charge Sector of 3d Parity-Violating CFTs
• Transition of Large $R$-Charge Operators on a Conformal Manifold
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Revisiting the AdS Boson Stars: the Mass-Charge Relations
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Bootstrap bound on extremal Reissner-Nordström black hole in AdS
• Numerical tests of the large charge expansion
• Sub-leading conformal dimensions at the O(4) Wilson-Fisher fixed point
• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
• Superfluids, vortices and spinning charged operators in 4d CFT
• The large charge expansion and AdS/CFT
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Global Symmetry and Maximal Chaos
• Large-Charge Limit of AdS Boson Stars with Mixed Boundary Conditions
• Large R-charge EFT correlators in N=2 SQCD
• Newton vs. Coulomb in AdS/CFT and the Weak Gravity Conjecture
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• Droplet-Edge Operators in Nonrelativistic Conformal Field Theories
• Identifying Large Charge Operators
• Exclusion Inside or at the Border of Conformal Bootstrap Continent
• Large charge operators at large spin from relativistically rotating vortices
• Boundary Conformal Field Theory at Large Charge
• Higher-form anomalies and state-operator correspondence beyond conformal invariance