📝 SummarXiv

Abstract

Conformal 3-point correlators of conserved currents play important roles in numerous directions. These correlators are fixed by conformal symmetry up to few parameters, which are known only at the leading order in the perturbative expansions. The major challenges are from the multi-loop Feynman integrals with three external momenta. In this work, we employ the method of subgraphs to compute the subleading order corrections to the conformal current 3-point correlators in the large $N$ expansion. We show that the method of subgraphs generates diagrammatic expansions for the conformal 3-point correlators, and it closely relates to the operator product expansions in momentum space. We verify the subgraph expansions of the conserved current 3-point correlators using the exact results in 3D. We demonstrate that the multi-loop 3-point Feynman integrals can be significantly simplified by taking the subgraph expansions. Due to the constraints from conformal symmetry, it suffices to keep the first few terms of the subgraphs to completely fix the subleading order corrections. We apply this method to compute the $1/N$ corrections to the current correlators $\langle JJJ\rangle$ in the critical $O(N)$ vector model and the Gross-Neveu-Yukawa model. We also compute the $1/N$ corrections to the coefficients in the current-current-scalar correlators $\langle JJ\sigma_{T}\rangle$ and $\langle JJ\sigma\rangle$ in the critical $O(N)$ vector model. We compare the perturbative result with the bootstrap data and discuss its application for the conductivity near the quantum critical point.