Charting the space of 3D CFTs with a continuous global symmetry

Abstract

We study correlation functions of a conserved spin-1 current $J_{\mu }$ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point functions $⟨J_{\mu }{J}_{\nu }{\mathcal{O}}_{\Delta ,\ell }⟩$ and the four point function $⟨J_{\mu }{J}_{\nu }{J}_{\rho }{J}_{\sigma }⟩$ and identify the minimal set of independent crossing symmetry conditions. We obtain a recurrence relation for conformal blocks for generic spin-1 operators in three dimensions. In the process, we improve several technical points, facilitating the use of recurrence relations. By applying the machinery of the numerical conformal bootstrap we obtain universal bounds on the dimensions of certain light operators as well as the central charge. Highlights of our results include numerical evidence for the conformal collider bound and new constraints on the parameters of the critical $O(2)$ model. The results obtained in this work apply to any unitary, parity-preserving three dimensional CFT.

67 pages, 18 figures

References in corpus (15)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Conformal collider physics: Energy and charge correlations
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Bounds in 4D Conformal Field Theories with Global Symmetry
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Central Charge Bounds in 4D Conformal Field Theory
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Bootstrapping 3D Fermions with Global Symmetries
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• More $\mathcal{N}=4$ superconformal bootstrap
• R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories

Cited by in corpus (12)

• Carving out OPE space and precise $O(2)$ model critical exponents
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Recursion relation for general 3d blocks
• New Developments in the Numerical Conformal Bootstrap
• Higher-Point Conformal Blocks in the Comb Channel
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• Bootstrapping traceless symmetric $O(N)$ scalars
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Bounds on Triangle Anomalies in (3+1)d
• The Parisi-Sourlas Uplift and Infinitely Many Solvable 4d CFTs
• Harmonic Analysis in d-dimensional Superconformal Field Theory