Vector model in various dimensions

Abstract

We study behaviour of the critical $O(N)$ vector model with quartic interaction in $2\le d\le 6$ 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 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 $6-\epsilon$ 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 OPE coefficient vanishes up to $\mathcal{O}(1/N^{3/2})$ order.

v2: revisions in section 5, added appendices B, C with more details, minor improvements, references added, v3: improvements in section 5, missing contributions in section 5.B added, additional discussion and references added, v4: published version, references added, discussion extended, formulas simplified

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Cited by in corpus (10)

• The critical O(N) CFT: Methods and conformal data
• A plane defect in the 3d O$(N)$ model
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• The bi-conical vector model at $1/N$
• The background field method and critical vector models
• Long-range fermions and critical dualities
• CFT data in the Gross-Neveu model
• Conformal correlators in the critical $O(N)$ vector model
• Long-Range Vector Models at Large N
• Critical long-range vector model in the UV