On C-J and C-T in the Gross-Neveu and O(N) models

Abstract

We apply large N diagrammatic techniques for theories with double-trace interactions to the leading corrections to C-J, the coefficient of a conserved current two-point function, and C-T, the coefficient of the stress-energy tensor two-point function. We study in detail two famous conformal field theories in continuous dimensions, the scalar O(N) model and the Gross-Neveu (GN) model. For the O(N) model, where the answers for the leading large N corrections to C-J and C-T were derived long ago using analytic bootstrap, we show that the diagrammatic approach reproduces them correctly. We also carry out a new perturbative test of these results using the O(N) symmetric cubic scalar theory in 6 - epsilon dimensions. We go on to apply the diagrammatic method to the GN model, finding explicit formulae for the leading corrections to C-J and C-T as a function of dimension. We check these large N results using regular perturbation theory for the GN model in 2 + epsilon dimensions and the Gross-Neveu-Yukawa model in 4 - epsilon dimensions. For small values of N, we use Pade approximants based on the 4 - epsilon and 2 + epsilon expansions to estimate the values of C-J and C-T in d = 3. For the O(N) model our estimates are close to those found using the conformal bootstrap. For the GN model, our estimates suggest that, even when N is small, C-T differs by no more than 2% from that in the theory of free fermions. We find that the inequality C-T(UV) > C-T(IR) applies both to the GN and the scalar O(N) models in d = 3.