[Math-Phys Seminar] Non-perturbative Schwinger-Dyson equation for DT/PT vertices

11. November 2025

Taro Kimura (Université Bourgogne Europe)

Non-perturbative Schwinger-Dyson equation for DT/PT vertices

Non-perturbative Schwinger-Dyson (SD) equation is a discrete analog of the loop equation appearing in matrix models and related models. It was initially discussed for the gauge theory partition function and, as in the case of the matrix models, it has a close relation to the underlying infinite-dimensional symmetry of the system. In this talk, I’d like to discuss the non-perturbative SD equation for the higher-dimensional gauge theory partition function, interpreted as the generating function of the DT and PT invariants (DT/PT vertices) for CY3 and CY4 varieties, and address its underlying quantum algebraic structure, which is a consequence of geometric representation theory of the corresponding algebra.