Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 107, Issue 1, Pages 1-30Publisher
SPRINGER
DOI: 10.1007/s11005-016-0893-z
Keywords
Supersymmetric gauge theories; Fermi gas, Matrix models; Quantum and spectral theory; Topological string
Categories
Funding
- INFN Research Project GAST
- INFN Research Project STFI
- PRIN Geometria delle varieta algebriche
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We explore a new connection between Seiberg-Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang-Mills theory in a self-dual background to the spectral determinant of an ideal Fermi gas. We show that the spectrum of this gas is encoded in the zeroes of the Painlev, function. In addition, we find that the Nekrasov partition function on this background can be expressed as an O(2) matrix model. Our construction arises as a four-dimensional limit of a recently proposed conjecture relating topological strings and spectral theory. In this limit, we provide a mathematical proof of the conjecture for the local geometry.
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