Scaling dimensions at large charge for cubic ${\varphi }^3$ theory in six dimensions

Abstract

The $O(N)$ model with scalar quartic interactions at its ultraviolet fixed point, and the $O(N)$ model with scalar cubic interactions at its infra-red fixed point are conjectured to be equivalent. This has been checked by comparing various features of the two models at their respective fixed points. Recently, the scaling dimensions of a family of operators of fixed charge $Q$ have been shown to match at the FPs up to $\mathcal{O}\left(\frac{1}{{\mathcal{N}}^2}\right)$at leading order (LO) and next-to-leading order (NLO) in $Q$ using a semiclassical computation which is valid to all orders in the coupling. Here we perform a complementary but overlapping comparison using a perturbative calculation in six dimensions, up to three-loop order in the coupling, to compare these critical scaling dimensions beyond NLO in $Q$, in fact to all relevant orders in $Q$. We also obtain the corresponding results at $\mathcal{O}\left(\frac{1}{{\mathcal{N}}^3}\right)$ for the cubic theory.

14 pages, 2 figures, reference added, typos corrected

References in corpus (2)

• The Epsilon Expansion Meets Semiclassics
• Large charge at large N