$1/N$ corrections to $\langle TJJ\rangle$ and $\langle TTT\rangle$ in the critical $O(N)$ vector and Gross--Neveu--Yukawa models

Abstract

We compute the subleading corrections in the $1/N$ expansion of the three-point functions $\langle TJJ\rangle$ and $\langle TTT\rangle$ in the three-dimensional critical $O(N)$ vector and Gross--Neveu--Yukawa models. We determine the coefficients of the two parity-even conformal structures and the corresponding conformal collider parameters. The calculation uses an expansion of momentum-space Feynman diagrams in a soft external momentum, together with the contact terms required by background gauge and metric sources. The sums of the structure coefficients reproduce the known current and stress-tensor two-point normalizations. We also compute these coefficients independently using the metric and mixed metric--gauge derivatives of the sphere free energy. Extrapolating the large $N$ results to the $O(2)$ vector model yields reasonably good agreement with recent numerical bootstrap bounds. At $N=2$, our $γ$ and $t_4$ predictions lie within the joint bootstrap region under weaker spectral assumptions; their deviations from the more restrictive interval midpoints are only $3.28\%$ and $4.44\%$, respectively. We discuss the implications for energy flux, high-frequency conductivity, and shear response near quantum criticality.