blocks_3d: Software for general 3d conformal blocks

Abstract

We introduce the software blocks_3d for computing four-point conformal blocks of operators with arbitrary Lorentz representations in 3d CFTs. It uses Zamolodchikov-like recursion relations to numerically compute derivatives of blocks around a crossing-symmetric configuration. It is implemented as a heavily optimized, multithreaded, C++ application. We give performance benchmarks for correlators containing scalars, fermions, and stress tensors. As an example application, we recompute bootstrap bounds on four-point functions of fermions and study whether a previously observed sharp jump can be explained using the "fake primary" effect. We conclude that the fake primary effect cannot fully explain the jump and the possible existence of a "dead-end" CFT near the jump merits further study.

arXiv comment33 pages + appendices

References in corpus (39)

• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• Spinning Conformal Correlators
• Projectors, Shadows, and Conformal Blocks
• Bootstrapping the O(N) Vector Models
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Spinning Conformal Blocks
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Carving Out the Space of 4D CFTs
• Radial Coordinates for Conformal Blocks
• Bootstrapping the O(N) Archipelago
• Carving out OPE space and precise $O(2)$ model critical exponents
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Weight Shifting Operators and Conformal Blocks
• Bootstrapping 3D Fermions
• Recursion Relations for Conformal Blocks
• Harmonic Analysis and Mean Field Theory
• Bootstrapping 3D Fermions with Global Symmetries
• The 3d Stress-Tensor Bootstrap
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• Conformal correlators of mixed-symmetry tensors
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• General Three-Point Functions in 4D CFT
• Casimir recursion relations for general conformal blocks
• On the four-point function of the stress-energy tensors in a CFT
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
• Recursion relation for general 3d blocks
• Searching for gauge theories with the conformal bootstrap
• Bootstrap experiments on higher dimensional CFTs
• Mixed Scalar-Current bootstrap in three dimensions
• New Methods for Conformal Correlation Functions
• Comments on Determinant Formulas for General CFTs
• Bounds on Triangle Anomalies in (3+1)d

Cited by in corpus (3)

• The Gross-Neveu-Yukawa Archipelago
• Helicity basis for three-dimensional conformal field theory
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions