Work

Exact results for scaling dimensions of neutral operators in scalar conformal field theories

Year: 2025

Type: article

Abstract: We determine the scaling dimension Δ n for the class of composite operators ϕ n in the λ ϕ 4 theory in d = 4 − ε taking the double scaling limit n → ∞ and λ → 0 with fixed λ n via a semiclassical approach. Our results resum the leading power of n at any loop order. In the small λ n regime we reproduce the known diagrammatic results and predict the infinite series of higher-order terms. For intermediate values of λ n we find that Δ n / n increases monotonically approaching a ( λ n ) 1 / 3 behavior in the λ n → ∞ limit. We further generalize our results to neutral operators in the ϕ 4 in d = 4 − ε , ϕ 3 in d = 6 − ε , and ϕ 6 in d = 3 − ε theories with O ( N ) symmetry.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/physrevd.111.l041701

Authors: Oleg Antipin, Jahmall Bersini, Francesco Sannino