blocks_3d: software for general 3d conformal blocks

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, multi-threaded, 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.

Automated summary

The software blocks_3d is introduced for computing four-point conformal blocks in 3d CFTs, utilizing Zamolodchikov-like recursion relations for numerical computations. Performance benchmarks are provided for correlators with scalars, fermions, and stress tensors. As an example application, bootstrap bounds on four-point functions of fermions are recomputed to investigate a previously observed jump, concluding that the fake primary effect cannot fully explain it and suggesting further study on the possible existence of a dead-end CFT near the jump.