Resurgence in Integrable Field Theories - Lecture 1

Explore the resurgent properties of integrable field theories in two dimensions through this comprehensive lecture. Begin with a brief recap of Borel resummations and a historical overview of perturbation theory in quantum field theory. Delve into basic resurgence concepts and their application to three well-known integrable field theories that are UV-free, develop a mass gap in the IR, admit a 1/N expansion, and exhibit renormalon singularities. Examine the interplay between resurgent properties and the 1/N expansion, focusing on the free energy in the presence of a chemical potential coupled to a conserved charge. Learn about exact computations using thermodynamic Bethe ansatz techniques and large N QFT methods, as well as results at finite N. Cover key topics including the Dyson argument, logic series, optimal truncation, and the Linear Theorem, providing a comprehensive understanding of resurgence in integrable field theories.