Bootstrapping currents and stress tensors in 3d CFTs

Abstract

We perform a numerical conformal bootstrap study of the mixed system of correlation functions involving a spin-1 $\mathrm{U}(1)$ current $J$ and the stress-energy tensor $T$ in parity-preserving 3d CFTs. We find universal bounds on the stress-tensor two-point function $c_T$, which numerically reproduce the conformal collider bounds on $⟨JJT⟩$ and $⟨TTT⟩$, as well as bounds on the leading parity-even and parity-odd scalar operator dimensions. Under mild assumptions, we determine the values of the $⟨JJT⟩$ and $⟨TTT⟩$ three-point functions in the $\mathrm{O}(2)$ vector model. The $⟨TTT⟩$ result is new and $⟨JJT⟩$ is consistent with a previous result in the literature.

14 pages + appendices, 5 figures