An Atlas for 3d Conformal Field Theories with a U(1) Global Symmetry

TL;DR

This paper develops a numerical bootstrap framework for 3d conformal field theories with a U(1) symmetry, providing bounds, exclusion plots, and indications of potential new theories.

Contribution

It introduces new OPE bounds and exclusion plots for 3d CFTs with U(1) symmetry, including analysis of known and novel theories.

Findings

Bounds on OPE coefficients for various models

Exclusion plots revealing known and potential new theories

Identification of kinks suggesting unknown CFTs

Abstract

We present a collection of numerical bootstrap computations for 3d CFTs with a U(1) global symmetry. We test the accuracy of our method and fix conventions through a computation of bounds on the OPE coefficients for low-lying operators in the free fermion, free scalar, and generalised free vector field theories. We then compute new OPE bounds for scalar operators in the Gross-Neveu-Yukawa model, $O(2)$ model, and large $N$ limit of the $O(N)$ model. Additionally, we present a number of exclusion plots for such 3d CFTs. In particular, we look at the space of even and odd parity scalar operators in the low-lying spectrum that are compatible with crossing symmetry. As well as recovering the known theories, there are some kinks that indicate new unknown theories.