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 results suggest a novel and still unexplored interplay between conformal symmetry and resurgence, offering an intuitive interpretation for the striking agreement of the large-charge predictions with lattice data, even in the case 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 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 results suggest a novel and still unexplored interplay between conformal symmetry and resurgence, offering an intuitive interpretation for the striking agreement of the large-charge predictions with lattice data, even in the case of the O(2) model.

We investigate the odd-even staggering in the harmonically-trapped unitary Fermi gas at large particle-number charge Q. Using both a large-NN BdG description and a complementary large-charge EFT method, we show that for odd particle number the extra fermion forms an edge-localized quasiparticle near the Thomas-Fermi surface rather than a bulk excitation. In the edge limit, the microscopic BdG problem reduces to a universal coupled Airy system whose lowest positive eigenvalue fixes the leading odd-even splitting energy, $\chi \xi^{1/6} (24 Q)^{1/9}$, where $ξ$ is the Bertsch parameter, and $\chi$ is a universal edge coefficient. The associated EFT describes a fermionic mode confined to the boundary and coupled to the superfluid Goldstone field, reproducing the same QQ scaling while introducing a dependence on two low-energy constants. Finally, we numerically compute the spectrum and confirm the predicted scaling and localization properties.

We study cusped Wilson line operators in the Abelian Higgs model in d = 4 − ε at large external charges. Using a double-scaling limit Q → ∞, ε → 0 with Q ε fixed, we develop a semiclassical framework that provides analytic control beyond fixed-order perturbation theory. We compute the cusp anomalous dimension for arbitrary charges up to next-to-next-to-leading order in the gauge coupling, while resumming scalar self-interactions to all orders. Our results interpolate between perturbative and large-charge regimes, accessing domains that are invisible in fixed-order perturbation theory. As an application, we provide new predictions for various defect CFT observables, including the Mandelstam-Schwinger-dressed two-point function characterizing the superconducting phase transition.

Cold-atom experiments which measure Fermi-gas properties near unitarity confine fermionic atoms to a region of space using trapping potentials of various shapes. The presence of a trapping potential introduces a new characteristic physical scale in the superfluid EFT which, inter alia, describes the acoustic branch of excitations in the far infrared well below the scale of the superfluid gap. In this EFT there is a clear hierarchy of scales, and corrections to the homogeneous system due to the trapping potential may be organized into three regions with distinct power counting that relies on both the EFT derivative expansion, and the WKB approximation, which is an expansion in gradients of the trapping potential. The energy spectrum of the superfluid system is obtained in each of the regions by explicit computation of the phonon-field fluctuations, and by the modifications to the dynamic structure factor due to the corresponding density fluctuations. The most significant deviations from linear dispersion due to the trapping potential are found in the far infrared region of the superfluid EFT.