On the six-loop scaling dimensions of the (ϕ2) operators in d = 3
Abstract
We consider a class of singlet operators ( ϕ 2 ) n in the three-dimensional O ( N ) model with λ 2 ϕ 6 interaction. Recently [1], the corresponding anomalous dimensions γ 2 n were computed by semiclassical methods and the all-loop result for the leading- n corrections in the small λ limit was found. In this paper, we obtain the six-loop expressions not only for the leading- n contribution but also for the subleading one. While the leading correction confirms the predictions of recent semiclassical calculation, the subleading one is a new result and will serve as a future welcome check for all-loop expressions. As an important by-product of our calculation, we provide a full dependence on n of the four-loop γ 2 n in the O ( N ) case.
Fields of Study & Subjects
Quantum Chromodynamics and Particle Interactions
Black Holes and Theoretical Physics
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Nuclear Physics B
- Publisher
- Elsevier BV
- Volume
- 1024
- Pages
- 117331–117331
- Publication date
- 31 January 2026
- Language
- EN