Classical irregular block, N=2 pure gauge theory and Mathieu equation

Understand

Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions.

• In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory.
• A missing element of that correspondence is identified with the classical irregular block.
• Explicit tests provide a convincing evidence that such a function exists.