SCGP Weekly Talk: Hiraku Nakajima, RIMS, Kyoto University

Hiraku Nakajima, RIMS, Kyoto University

Title: Representation Theory and Gauge Theory
Speaker: Hiraku Nakajima, RIMS, Kyoto University
Date: Tuesday, October 8, 2013
Time: 1:00pm – 2:00pm
Place: Lecture Hall 102, Simons Center

 

 

 

Abstract: The gauge theory is a quantum field theory based on the theory of connections on principal bundles over the space-time. The Lie group appears as a structure group of principal bundles. In particular, the representation theory of Lie groups has been used in the gauge theory as a language. In the last few decades, much deeper links between gauge theory and representation theory have been developed. Not only local symmetry of the gauge theory is controlled by a Lie group, more global structures of the theory can be understood by representation theory of a Lie group or a related algebra, which is usually different from the original one. I will explain that the W-algebra (a generalization of Virasoro algebra) appears two seemingly unrelated gauge theories in 2d and 4d (the AGT
correspondence).