C_{T} and C_{J} up to next-to-leading order in 1/N in the Conformally Invariant O(N) Vector Model for 2<d<4

TL;DR

This paper computes the next-to-leading order 1/N corrections to the central charge C_T and the current coefficient C_J in the conformally invariant O(N) vector model for dimensions between 2 and 4, using operator product expansions and graphical methods.

Contribution

It provides the first calculation of C_T and C_J at next-to-leading order in 1/N for the O(N) model in 2<d<4, extending previous results and testing conformal field theory expectations.

Findings

Calculated C_T and C_J at next-to-leading order in 1/N for 2<d<4.

Results agree with generalized C- and k-theorems in higher dimensions.

Consistent with known three-loop calculations in -psilon  theory.

Abstract

Using Operator Product Expansions and a graphical ansatz for the four-point function of the fundamental field \phi^{\alpha}(x) in the conformally invariant O(N) vector model, we calculate the next-to-leading order in 1/N values of the quantities C_{T} and C_{J}. We check the results against what is expected from possible generalisations of the C- and k-theorems in higher dimensions and also against known three-loop calculations in a O(N) invariant \phi^{4} theory for d=4-\epsilon.