Analyticity of Nekrasov Partition Functions

Abstract

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.

37 pages, minor corrections

References in corpus (5)

• Asymptotically free N=2 theories and irregular conformal blocks
• Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state
• Quantum Algebras and Cyclic Quiver Varieties
• Representation Homology, Lie Algebra Cohomology and Derived Harish-Chandra Homomorphism
• Norm of the Whittaker vector of the deformed Virasoro algebra

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