Cluster Integrable Systems and Five-Dimensional BPS Spectra

25.05.2023 11:00

In this talk, I will demonstrate how discrete cluster integrable systems can provide a comprehensive understanding of the stable BPS particle spectrum in five-dimensional theories on a circle. These theories emerge from the geometric engineering of M-theory on toric Calabi-Yau threefolds. While their BPS spectrum is typically "wild", with an infinite number of states of arbitrarily high spin, specific algebraic solutions of the integrable systems indicate the existence of "tame" chambers. In these chambers, the BPS spectrum can be expressed in closed form and comprises vectormultiplets, infinite towers of hypermultiplets, and Kaluza-Klein states. By utilizing wall-crossing formulas, it becomes possible to obtain the spectrum in any other chamber. To illustrate this methodology, I will examine the concrete example of local del Pezzo threefolds, geometrically engineering SU(2) Super Yang-Mills with matter, and their corresponding q-Painleve' cluster integrable system. Additionally, time permitting, I will briefly discuss the interpretation of the aforementioned results through the lens of WKB approximation for q-difference equations.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Physical Mathematics Seminar Series"

entrée libre