Towards 3D CFT Cartography with the Stress Tensor Bootstrap

TL;DR

This paper uses the stress tensor bootstrap to map the landscape of three-dimensional conformal field theories, revealing sharp features that may correspond to both known and unknown CFTs, advancing the systematic exploration of these theories.

Contribution

It introduces a new numerical approach to explore 3D CFTs, identifying features that suggest the existence of many potentially unknown theories.

Findings

Identification of sharp features like kinks and ridges in bounds

Some features match known CFTs, others suggest new theories

Features are robust to increased numerical precision

Abstract

We present new numerical results on the space of local, unitary, parity-preserving conformal field theories (CFTs) in three dimensions from the stress tensor bootstrap. In bounds maximizing certain OPE coefficients, we find a plethora of sharp features, such as kinks and ridges, as a function of scaling dimensions. We show that some of these features correspond to known theories, but there are many others that are equally strong but do not match known CFTs. We argue that these features are robust to raising numerical order and could then correspond to numerous as yet unknown CFTs. We conclude in proposing a program of "CFT cartography": the systematic exploration of the landscape of CFTs without individual theory targets in mind.