On CJ and CT in the Gross–Neveu and O(N) models. (14th September 2016) - Diab, Kenan; Fei, Lin; Giombi, Simone; Klebanov, Igor R; Tarnopolsky, Grigory
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 − ϵ 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 + ϵ dimensions and the Gross–Neveu–Yukawa model in 4 − ϵ dimensions. For small values of N, we use Padé approximants based on the 4 − ϵ and 2 + ϵ 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.