blocks_3d: Software for general 3d conformal blocks

TL;DR

The paper introduces blocks_3d, a highly optimized C++ software for computing four-point conformal blocks in 3d CFTs, enabling advanced bootstrap analyses and exploring the fake primary effect in fermionic correlators.

Contribution

It presents a new software tool, blocks_3d, capable of efficiently computing conformal blocks for arbitrary Lorentz representations in three dimensions.

Findings

Benchmarks show high performance for scalar, fermion, and stress tensor correlators.

Recomputed bootstrap bounds indicating the fake primary effect does not fully explain observed jumps.

Identified the potential for a 'dead-end' CFT near the jump, suggesting further research directions.

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.