2019/11/30 by Mikhail Goykhman, Michael Smolkin
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Dimension (graph theory) #Field (mathematics) #Fixed point #Function (biology) #Geometry #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Operator product expansion #Order (exchange) #Physics #Product (mathematics) #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quartic function #hep-th
paper · pdf · doi:10.1103/physrevd.102.025003
published as Phys. Rev. D 102, 025003 (2020) · 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
openalex publication_date 2020/07/06 · arxiv created 2020/07/08 · arxiv updated 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study behavior of the critical O(N) vector model with quartic interaction in 2\ensuremath≤d\ensuremath≤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 nontrivial fixed point and explore the corresponding conformal field theory (CFT). In particular, we use conformal techniques to calculate the multiloop 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\ensuremath-\ensuremathε 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 operator product expansion coefficient vanishes up to O(1/N3/2) order.