# A safe CFT at large charge

## TL;DR

This paper investigates a four-dimensional gauge-Yukawa theory at large global charge, revealing its low-energy spectrum, symmetry breaking, and conformal dimensions through a triple expansion approach, providing new insights into its conformal properties.

## Contribution

It applies the large-charge limit to a novel 4D gauge-Yukawa theory with an ultraviolet fixed point, deriving spectrum, symmetry breaking, and conformal dimensions.

## Key findings

- Fermions decouple at low energy, leaving a confining Yang-Mills sector.
- Spectrum includes relativistic and non-relativistic Goldstone bosons.
- Established conformal dimensions via a triple expansion in charge, flavors, and inverse coupling.

## 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.