Boot strapping 3D fermions with global symmetries

Abstract

We study the conformal bootstrap for 4-point functions of fermions <psi(i)psi(j)psi(k)psi(l)> in parity-preserving 3d CFTs, where psi(i) transforms as a vector under an O(N) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N. For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.