The large charge approach allows to describe special sectors of strongly-coupled systems. When another controlling parameter is present, it is still useful because it allows to unveil interesting mathematical structures and access previously unexplored parts of the spectrum. In this talk I will concentrate on the bosonic O(N) vector model and the fermionic NJL model in the large-N limit, give a geometrical interpretation of the asymptotic expansion of the dimension of the lowest operator of fixed charge, and use resurgence to resum this expansion. The result suggests a still unexplored interplay between conformal symmetry and resurgence and will lead to an intuitive interpretation for the impressive agreement of the large-charge predictions with lattice data also in the O(2) model case.

Working in sectors of large global charge leads to important simplifications when studying strongly coupled CFTs. In this talk I will introduce the large-charge expansion via the simple example of the O(2) model

The large charge approach allows to describe special sectors of strongly-coupled systems. When another controlling parameter is present, it is still useful because it allows to unveil interesting mathematical structures and access previously unexplored parts of the spectrum. In this talk I will concentrate on the O(N) vector model in the large-N limit, give a geometrical interpretation of the asymptotic expansion of the dimension of the lowest operator of fixed charge, and use resurgence to resum this expansion. The result suggests an unexpected interplay between conformal symmetry and resurgence and will lead to an intuitive interpretation for the impressive agreement of the large-charge predictions with lattice data also in the O(2) model case. Based on 1610.04495, 2008.03308, 2102.12488.

Working in a sector of large charge is a powerful tool to analytically access models that are either strongly coupled or otherwise difficult to solve explicitly. In the context of integrable systems, Volin’s method is exactly such a large-charge approach. In this note, we apply this method to the bi-Yang-Baxter deformed SU(2) principal chiral model. Our main result is an explicit expression for the free energy density as an asymptotic expansion. We moreover determine the leading non-perturbative effects both via analytic methods and a resurgence analysis.

The utility of the non-relativistic large-charge EFT for physical systems, and neutron matter in particular, relies on controlled Schrödinger-symmetry breaking deformations due to scattering length and effective-range effects in the two-body system. A recently-found exact solution of the large-charge system is used to compute these effects for two-point correlation functions of large-charge operators in perturbation theory around the large-charge ground state. Notably, the leading effective-range effects are found to enter at second order in the effective range, in agreement with analogous calculations in the three-body system. The Schrödinger-symmetry breaking deformations are used – together with input from Quantum Monte Carlo simulations – to address the range of validity of the EFT with deformations both in general and in the special case of neutron matter. In particular, it is found that nuclear reactions with up to six low-energy neutrons in the final state can be described by the large-charge EFT with Schrödinger-symmetry breaking.

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in non-relativistic conformal field theory is obtained. This field is used to compute Schr"odinger-invariant n-point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schrödinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large-N expansion at large charge.