A safe CFT at large charge

Abstract

We apply the large-charge limit to the first known example of a four-dimensional gauge-Yukawa theory featuring an ultraviolet interacting fixed point in all couplings. We determine the energy of the ground state in presence of large fixed global charges and deduce the global symmetry breaking pattern. We show that the fermions decouple at low energy leaving behind a confining Yang-Mills theory and a characteristic spectrum of type I (relativistic) and type II (non-relativistic) Goldstone bosons. Armed with the knowledge acquired above we finally arrive at establishing the conformal dimensions of the theory as a triple expansion in the large-charge, the number of flavors and the controllably small inverse gauge coupling constant at the UV fixed point. Our results unveil a number of noteworthy properties of the low-energy spectrum, vacuum energy and conformal properties of the theory. They also allow us to derive a new consistency condition for the relative sizes of the couplings at the fixed point.

arXiv comment18 pages, published version, some typos corrected

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Cited by in corpus (22)

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• Charging the Walking U(N)$\times$U(N) Higgs Theory as a Complex CFT
• Resurgence of the large-charge expansion
• Near-Conformal Dynamics at Large Charge
• Charging the Conformal Window
• More on the Weak Gravity Conjecture via Convexity of Charged Operators
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• Safety versus triviality on the lattice
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• The free and safe fate of symmetry non-restoration
• Yukawa interactions at Large Charge
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Superfluids, vortices and spinning charged operators in 4d CFT
• The analytic structure of the fixed charge expansion
• Asymptotic safety in the Litim-Sannino model at four loops
• Identifying Large Charge Operators
• Charging the conformal window at nonzero $\theta$ angle
• Safe Hologram