Abstract
Nekrasov partition function for the supersymmetric gauge theories with general Lie groups is not so far known in a closed form while there is a definition in terms of the integral. In this paper, as an intermediate step to derive it, we give a recursion formula among partition functions, which can be derived from the integral. We apply the method to a toy model which reflects the basic structure of partition functions for BCD type Lie groups and obtained a closed expression for the factor associated with the generalized Young diagram.
Highlights
Starting from a seminal work by Seiberg and Witten [1], the connection between supersymmetric gauge theories in 4D and 2D conformal field theories is getting more and more tight
They were written as a sum over factors associated with Young diagrams which implied the connection with 2D theories
Such correspondence becomes more explicit by the AGT conjecture [4] where the partition function is directly related to the correlation function of Liouville theory
Summary
Starting from a seminal work by Seiberg and Witten [1], the connection between supersymmetric gauge theories in 4D and 2D conformal field theories is getting more and more tight. The first key step in such direction is the explicit derivation of instanton partition function by Nekrasov and others in the omega background [2, 3] They were written as a sum over factors associated with (a set of) Young diagrams which implied the connection with 2D theories. We give a partial answer to these problems. We derive the recursive relation in a similar form and give the explicit form of the residue as a product of factors for generalized Young diagrams. We give some arguments how to fight with other problems by using our strategy
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
