Correlation Functions in Integrable Supersymmetric Gauge Theories - Integrability vs. Localisation

Explore the intersection of integrability and supersymmetric localization in this advanced physics lecture examining correlation functions in N=2 super-conformal gauge theories. Delve into the quantum structure of strongly interacting supersymmetric gauge theories through two complementary approaches that have emerged from decades of research guided by string theory dualities. Investigate the recently discovered common structures that appear when both supersymmetric localization and integrability methods are applied to N=2 super-conformal theory in four dimensions, specifically the theory obtained as a Z_K orbifold of N=4 super Yang-Mills theory. Learn how special three-point functions in N=2 SYM theory, initially computed through localization in terms of Fredholm determinants, can be derived using the integrability approach originally developed for N=4 SYM theory. Understand the natural emergence of Fredholm determinants within the integrability framework and discover the deeper underlying structures that connect localization and integrability methods in supersymmetric gauge theory calculations.