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arXiv · 2112.01196

Scaling dimensions at large charge for cubic $\phi^3$ theory in six dimensions

I. Jack·D. R. T. Jones
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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 $\cal{O}\left(\frac{1}{N^2}\right)$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 $\cal{O}\left(\frac{1}{N^3}\right)$ for the cubic theory.

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I. Jack, D. R. T. Jones. 2021-12-02. Scaling dimensions at large charge for cubic $\phi^3$ theory in six dimensions. https://doi.org/10.1103/physrevd.105.045021

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