Charging the $O(N)$ model

Abstract

We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in 4-$\epsilon$ dimensions to the leading and next to leading order terms in the charge expansion but to all-orders in the coupling. We test our results to the maximum known order in perturbation theory while determining higher order terms.

arXiv comment6 pages. v2 Added the 4-loop anomalous dimension of spin-0 operators transforming in the traceless symmetric O(N) representations; corrected some formulae while the rest matches the PRD version

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• The OPE meets semiclassics
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• The Breakdown of Resummed Perturbation Theory at High Energies
• Gauge Invariance at Large Charge
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture
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