Refined Instanton Analysis for Asymptotically Free QFTs and Mass Gap

Instantons are an important source of nonperturbative effects in quantum field theories, but their role in asymptotically free theories has not been well understood. In this talk, we will present a new approach to instanton analysis in the context of 2d $CP^N$ sigma models.  From this, we will show that, contrary to common belief, instantons can in fact capture the vacuum structure and non-perturbative properties such as mass gap, fractional theta dependence, and confinement. In the supersymmetric sigma model, our method gives a new derivation of the mirror symmetry and the Landau-Ginzburg dual theory. Our construction also demonstrates that there is no conflict between large N and instantons.