Vector model in various dimensions

Mikhail Goykhman, Michael Smolkin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We study behavior of the critical O(N) vector model with quartic interaction in 2≤d≤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-ϵ 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.

Original languageAmerican English
Article number025003
JournalPhysical Review D
Issue number2
StatePublished - 15 Jul 2020

Bibliographical note

Funding Information:
We thank Noam Chai, Soumangsu Chakraborty, Johan Henriksson, Zohar Komargodski and Anastasios Petkou for helpful discussions and correspondence. We would like to express our special thanks of gratitude to Simone Giombi, Igor Klebanov and Gregory Tarnopolsky for numerous comments and stimulating correspondence which helped us to improve our results and their presentation. This work is partially supported by the Binational Science Foundation (Grant No. 2016186), the Israeli Science Foundation Center of Excellence (Grant No. 2289/18) and by the Quantum Universe I-CORE program of the Israel Planning and Budgeting Committee (Grant No. 1937/12).

Publisher Copyright:
© 2020 authors. Published by the American Physical Society.


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