Classical limit of irregular blocks and Mathieu functions

Understand

The Nekrasov-Shatashvili limit of the N=2 SU(2) pure gauge (Omega-deformed) super Yang-Mills theory encodes the information about the spectrum of the Mathieu operator.

• On the other hand, the Mathieu equation emerges entirely within the frame of two-dimensional conformal field theory (2d CFT) as the classical limit of the null vector decoupling equation for some degenerate irregular block.
• Therefore, it seems to be possible to investigate the spectrum of the Mathieu operator employing the techniques of 2d CFT.
• To exploit this strategy, a full correspondence between the Mathieu equation and its realization within 2d CFT has to be established.