Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz

Understand

In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations.

• In this work we present an explicit derivation of this fact as well as generalizations to quiver gauge theories.
• To do so we combine various techniques like the iterated Mayer expansion, the method of expansion by regions, and the path integral tricks for non-perturbative summation.
• The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems.