Nonperturbative physics in sigma models

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Two-dimensional sigma models are prominent strongly coupled systems sharing asymptotic freedom, a dynamically generated mass-gap and other important properties with Quantum chromodynamics. Recently, two very interesting nonperturbative effects have been studied in these systems: the cancellation of perturbative renormalon singularities by fractional instanton contributions and the generation of a nonzero charge density by a chemical potential through a formulation in terms of dual variables. Both topics shall be advanced in this project, mainly using lattice techniques. Discretisations on space-time lattices are one of the very few ab initio approaches to nonperturbative physics. The project aims at checking the renormalon conjecture in these models numerically as well as further developing dual variables for structural questions and specific simulations at nonzero density and beyond.