Mathematics and Physics of BPS-states

Nikita Nekrasov holds one of the prestigious professorships at the Simons Center for Geometry of Physics at Stony Brook University, New York, USA. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be a visiting professor at the Department of Mathematics, Uppsala University.

Nikita Nekrasov is world renown for his work on supersymmetric gauge theories and the Nekrasov partition function bears his name.

In the supersymmetric models for the smallest constituents of the universe, quantum states with smallest possible mass for given topological charge play a central role. Such states are known as BPS-states and were first described by Bogomolnyi, Prasad, and Sommerfield in the context of magnetic monopoles in 1975. In general, BPS-states are solutions to comparably simple differential equations and therefore often allows for exact descriptions.  

The project aims to understand connections between BPS states in four-dimensional quantum field theories and conformal field theory in two dimensions. This is an aspect of Nekrasov’s BPS/CFT-correspondence with origins in string theory and which leads to mathematical descriptions of complex quantum phenomena. A goal for the project is to gain mathematical control of the theories by using probability theory to describe the moduli space of BPS-instantons and how it relates to conformal blocks and partition functions. The project thereby aims for new insights about the structure of space time and the foundations of quantum field theory.   

Photo: Sean Lewthwaite/Nina Mikhailyuk