Seiberg-Witten theory as a Fermi gas

Understand

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 Omega-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 Painleve III tau 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.