Analyticity of Nekrasov Partition Functions

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...

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Bibliographic Details
Published in:Communications in mathematical physics 2018-12, Vol.364 (2), p.683-718
Main Authors: Felder, Giovanni, Müller-Lennert, Martin
Format: Article
Language:English
Subjects:
Analytic functions
Classical and Quantum Gravitation
Complex Systems
Deformation
Field theory
Gauge theory
Mathematical analysis
Mathematical and Computational Physics
Mathematical Physics
Parameters
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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 Moore, Nekrasov, and Shatashvili, which we also prove.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3270-1