Charging the Walking U(N)$\times$U(N) Higgs Theory as a Complex CFT

Abstract

We apply a semi-classical method to compute the conformal field theory (CFT) data for the U(N)xU(N) non-abelian Higgs theory in four minus epsilon dimensions at its complex fixed point. The theory features more than one coupling and walking dynamics. Given our charge configuration, we identify a family of corresponding operators and compute their scaling dimensions which remarkably agree with available results from conventional perturbation theory validating the use of the state-operator correspondence for a complex CFT.

arXiv comment7 pages

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• General scalar renormalisation group equations at three-loop order
• Anomalous dimensions at large charge in d=4 O(N) theory
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• Transition of Large $R$-Charge Operators on a Conformal Manifold
• Yukawa interactions at Large Charge
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions
• Operator spectrum of nonrelativistic CFTs at large charge
• Six-loop anomalous dimension of the ${\varphi }^Q$ operator in the $O(N)$ symmetric model
• Large-Charge Limit of AdS Boson Stars with Mixed Boundary Conditions
• The Breakdown of Resummed Perturbation Theory at High Energies
• Gauge Invariance at Large Charge
• Boundary Conformal Field Theory at Large Charge
• Convexity, large charge and the large-N phase diagram of the ${\phi }^4$ theory