Trans-series in Quantum Field Theory: SVZ Approach and Applications

This lecture provides an overview of the SVZ sum rules, which are an analytic approach to non-perturbative quantum field theory (QFT). The instructor discusses how these rules combine operator product expansion with vacuum condensates to compute exponentially small corrections to perturbative series in QFT. The lecture emphasizes the significance of trans-series in QFT, particularly in the context of resurgence theory. The instructor presents a precision test of the SVZ approach using the Gross-Neveu model, where exact trans-series can be derived from large N methods. The discussion includes the physical origins of non-perturbative corrections, such as instantons and renormalons, and how they relate to the factorial divergence of perturbation theory. The lecture concludes with a detailed examination of the Gross-Neveu model, highlighting the role of two-quark and four-quark condensates in understanding non-perturbative effects and the validity of the SVZ method in capturing fundamental physics.