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A safe CFT at large charge
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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.
Forward citations
Cited by 4 Pith papers
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Large charge at large N
A saddle-point evaluation of the O(2N) Wilson-Fisher partition function yields the large-charge conformal dimension and finite-temperature free energy in the regime 1 << N << Q, including the universal Q^0 Casimir term.
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Accessing Large Global Charge via the $\epsilon$-Expansion
The lowest operator dimension at large global charge in the O(2) Wilson-Fisher model is derived to leading order in 1/J and epsilon, giving 0.293 J^(3/2) at D = 3 and a crossover controlled by lambda = J epsilon.
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The large charge limit of scalar field theories and the Wilson-Fisher fixed point at $\epsilon=0$
In the double scaling limit g to 0, n to infinity at fixed lambda = g n^2, the dimension of the charge n operator phi^n in the O(2) Wilson-Fisher theory is exactly n + lambda/(32 pi^2).
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Safety versus triviality on the lattice
For SU(2) with 24 and 48 Dirac flavors, the lattice gradient-flow coupling matches the perturbative two-loop running at accessible scales and refuses to grow large, which is compatible with a Landau pole but does not ...
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