Title: Cluster Integrable Systems and Five-Dimensional BPS Spectra

Speaker: Dr. Fabrizio Del Monte

Affiliation: University of Sheffield, UK （英国谢菲尔德大学）

Time: 16:00-17:00, Tuesday, 17th October, 2023 (UTC+8, Beijing Time)

Venue: Zoom Meeting (ID: 385 442 0225; Passcode: yauc)

Inviter: Jie Gu （顾杰）

Abstract  

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, associated to gauge theory phases. In these chambers, the BPS spectrum can be expressed in closed form and comprises vector multiplets, 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.

Speaker

Dr. Fabrizio Del Monte got his PhD from SISSA, Italy, in 2020 under the supervision of Giulio Bonelli and Alessandro Tanzini. Following this, he was a CRM-ISM postdoctoral fellow at the Centre de Recherches Mathématiques in Montréal, before moving to the University of Sheffield in 2023 as a postdoctoral fellow. His research interests include Integrable Systems, String Theory, Stability Conditions and BPS states, Conformal Field Theory.