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

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.