Vector model in various dimensions
Mikhail Goykhman, Michael Smolkin

TL;DR
This paper investigates the critical $O(N)$ vector model across various dimensions using large-$N$ expansion, deriving new conformal field theory data and confirming consistency with alternative models.
Contribution
It provides the first detailed multi-loop conformal calculations for the $O(N)$ model in general dimensions and explores the model's fixed points and CFT data.
Findings
Evidence for a non-trivial fixed point in the model.
Calculation of new CFT data for the three-point function.
Matching results with alternative scalar models in 6 - ε dimensions.
Abstract
We study behaviour of the critical vector model with quartic interaction in dimensions to the next-to-leading order in the large- expansion. We derive and perform consistency checks that provide an evidence for the existence of a non-trivial fixed point and explore the corresponding CFT. In particular, we use conformal techniques to calculate the multi-loop 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 dimensions our results match their counterparts obtained within a proposed alternative description of the model in terms of massless scalars with cubic interactions. In we find that the OPE coefficient vanishes up to order.
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