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

Abstract

Recently it was shown that the scaling dimension of the operator ${\varphi }^n$ in $\lambda (\bar{\varphi }\varphi {)}^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$, 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.

8 figures, 5 tables, 24 pages. arXiv admin note: text overlap with arXiv:2101.09820

References in corpus (11)

• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Three Loop Analysis of the Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Selected Topics in the Large Quantum Number Expansion
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Generalized Wilson-Fisher critical points from the conformal OPE
• Charging the $O(N)$ model
• Charging the Walking U(N)$\times$U(N) Higgs Theory as a Complex CFT
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• Anomalous dimensions for ${\varphi }^n$ in scale invariant $d=3$ theory
• Anomalous dimensions at large charge in d=4 O(N) theory
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model

Cited by in corpus (6)

• Yukawa interactions at Large Charge
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Spinning correlators in large-charge CFTs
• Six-loop anomalous dimension of the ${\varphi }^Q$ operator in the $O(N)$ symmetric model
• The analytic structure of the fixed charge expansion
• Convexity, large charge and the large-N phase diagram of the ${\phi }^4$ theory