Identifying Large Charge Operators

Abstract

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge $n^{-1}$, between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order $n^{1/2}$ while the computation of observables is valid up to spins of order $n$. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum.

arXiv comment45 pages + appendices, 5 figures

References in corpus (19)

• Conformal Partial Waves and the Operator Product Expansion
• The Analytic Bootstrap and AdS Superhorizon Locality
• Convexity and Liberation at Large Spin
• Radial Coordinates for Conformal Blocks
• Semiclassics, Goldstone Bosons and CFT data
• The Epsilon Expansion Meets Semiclassics
• Conformal Bootstrap At Large Charge
• Semiclassical approach for multiparticle production in scalar theories
• Large charge at large N
• The local Callan-Symanzik equation: structure and applications
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• The large charge limit of scalar field theories and the Wilson-Fisher fixed point at $\epsilon =0$
• Rotating superfluids and spinning charged operators in conformal field theory
• A safe CFT at large charge
• The OPE meets semiclassics
• Correlation functions in scalar field theory at large charge
• Free field primaries in general dimensions: Counting and construction with rings and modules
• Spinning correlators in large-charge CFTs
• The analytic structure of the fixed charge expansion

Cited by in corpus (2)

• Large charge operators at large spin from relativistically rotating vortices
• Higher-form anomalies and state-operator correspondence beyond conformal invariance