Seiberg–Witten theory as a Fermi gas

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 Painlevé

\mathrm{III}_3

\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. In this limit, we provide a mathematical proof of the conjecture for the local

{\mathbb P}^1 \times {\mathbb P}^1

geometry.

Note:

25 pages. v3: misprints corrected,references added

Supersymmetric gauge theories
Fermi gas
Matrix models
Quantum and spectral theory
Topological string
string: topological
statistics: quantum
Seiberg-Witten model
Fermi gas
spectral

References(0)

Figures(0)

Loading ...