Trans-series in Quantum Field Theory: SVZ Approach Overview

This lecture provides an overview of the Shifman-Vainshtein-Zakharov (SVZ) method, which combines operator product expansion with vacuum condensates to compute non-perturbative corrections in quantum field theory (QFT). The instructor discusses the significance of perturbation theory and the emergence of non-perturbative effects, particularly exponentially small corrections. The lecture highlights the role of renormalons as indicators of these corrections and introduces the SVZ method as a tool for calculating power corrections in quantum chromodynamics (QCD). The instructor presents a precision test of the SVZ approach using the Gross-Neveu model, demonstrating how exact trans-series can be derived from large N methods. The discussion includes the implications of vacuum condensates and the challenges of accurately reproducing non-perturbative physics. The lecture concludes with reflections on the effectiveness of the SVZ method in capturing fundamental aspects of non-perturbative physics and the ongoing exploration of fractional power corrections in integrable models.