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arXiv · 2108.11161

Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions

I. Jack·D. R. T. Jones
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Abstract

Recently it was shown that the scaling dimension of the operator $ϕ^n$ in $λ(\barϕϕ)^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-ε$, for generic values of $λn$, and this was verified to two loop order in perturbation theory at leading and subleading $n$. This result was subsequently generalised to operators of fixed charge $Q$ in $O(N)$ theory and verified up to four loops in perturbation theory at leading and subleading $Q$. More recently, similar semiclassical calculations have been performed for the classically scale-invariant $U(N)\times U(N)$ theory in four dimensions, and verified up to two loops, once again at leading and subleading $Q$. Here we extend this verification to four loops. We also consider the corresponding classically scale-invariant theory in three dimensions, similarly verifying the leading and subleading semiclassical results up to four loops in perturbation theory.

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I. Jack, D. R. T. Jones. 2021-08-25. Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions. https://doi.org/10.1103/physrevd.104.105017

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