Vector model in various dimensions

We study behavior of the critical O(N) vector model with quartic interaction in 2≤d≤6 dimensions to the next-to-leading order in the large-N expansion. We derive and perform consistency checks that provide an evidence for the existence of a nontrivial fixed point and explore the corresponding conformal field theory (CFT). In particular, we use conformal techniques to calculate the multiloop diagrams up to and including 4 loops in general dimension. These results are used to calculate a new CFT data associated with the three-point function of the Hubbard-Stratonovich field. In 6-ϵ dimensions our results match their counterparts obtained within a proposed alternative description of the model in terms of N+1 massless scalars with cubic interactions. In d=3 we find that the operator product expansion coefficient vanishes up to O(1/N3/2) order.