Analyticity of Nekrasov Partition Functions

Understand

We prove that the K-theoretic Nekrasov instanton partition functions have a positive radius of convergence in the instanton counting parameter and are holomorphic functions of the Coulomb parameters in a suitable domain.

• We discuss the implications for the AGT correspondence and the analyticity of the norm of Gaiotto states for the deformed Virasoro algebra.
• The proof is based on random matrix techniques and relies on an integral representation of the partition function, due to Nekrasov, which we also prove.