Abstract
We use the background field method to systematically derive CFT data for the critical ϕ6 vector model in three dimensions, and the Gross-Neveu model in dimensions 2 ≤ d ≤ 4. Specifically, we calculate the OPE coefficients and anomalous dimensions of various operators, up to next-to-leading order in the 1/N expansion.
Highlights
Become analytically controllable in the large N framework
In the process of this study we found that, while the anomalous dimensions in critical vector models have been extensively studied, there has been much less study of the conformal three-point functions
We find that our method of computation — in particular, applying the background field method [29] in the context of large N conformal perturbation theory — provides a simple and coherent framework
Summary
Consider the following three-dimensional O(N ) vector model with sextic interaction, S=. The Feynman rules for the cubic interactions in (2.2), φ2σ and ρ3, are shown in figure 1. They generate kinetic terms for σ and ρ, respectively. We are going to use the background field method to calculate the effective cubic vertex in the effective action, at next-to-leading order in the 1/N expansion. In preparation for this, here we establish an additional Feynman rule in the presence of a background field ρ(x), i.e. we substitute ρ → ρ + ρinto (2.2) to get an action in the presence of ρ(x).
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