Anomalous dimensions for ${\varphi }^n$ in scale invariant $d=3$ theory

Abstract

Recently it was shown that the scaling dimension of the operator ${\varphi }^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading $n$. Here we extend this verification to six loops, once again at leading and subleading $n$. We then perform a similar exercise for a theory with a multiplet of real scalars and an $O(N)$ invariant hexic interaction. We also investigate the strong-coupling regime for this example.

arXiv comment25 pages, 8 figures, 4 tables. Uses tikz. Minor corrections and additions made

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• The OPE meets semiclassics
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• Yukawa interactions at Large Charge
• Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions
• The tricritical Ising CFT and conformal bootstrap
• The analytic structure of the fixed charge expansion
• Sextic tensor model in rank $3$ at next-to-leading order
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture
• On the six-loop scaling dimensions of the $({\varphi }^2{)}^n$ operators in $d=3$
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions