The background field method and critical vector models

We use the background field method to systematically derive CFT data for the critical $ϕ^6$ vector model in three dimensions, and the Gross-Neveu model in dimensions $2\leq d \leq 4$. Specifically, we calculate the OPE coefficients and anomalous dimensions of various operators, up to next-to-leading order in the $1/N$ expansion.

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