Abstract
We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the non-perturbative corrections and to extend the validity of the eft to any value of the charge. We conjecture the general form of the non-perturbative behavior of the conformal dimensions for any value of N and find very good agreement with previous lattice data.
Highlights
From the effective field theory point of view, there seems to no reason for the large-charge predictions to keep working for small charges
We develop a geometric picture interpreting the exponential corrections to the perturbative series as worldline instantons describing a particle of mass equal to the chemical potential μ moving along geodesics
We have studied in detail the cases of the model compactified both on the two-torus and the two-sphere which, via the state-operator correspondence allows to compute the conformal dimension of the lowest operator of charge q
Summary
We start with the Landau-Ginzburg model for 2N real scalar fields in the vector representation of O(2N ) (which we encode as N complex fields) in (1 + 2) dimensions with Euclidean signature on (R × M), where M is a Riemann surface. Including all terms up to mass dimension three, we have. This model flows to the wf fixed point in the infrared (ir) limit u → ∞ when r is fine-tuned to the value of the conformal coupling
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