Opers and TBA

Understand

In this note we study the "conformal limit" of the TBA equations which describe the geometry of the moduli space of four-dimensional N=2 gauge theories compactified on a circle.

• We argue that the resulting conformal TBA equations describe a generalization of the oper submanifold in the space of complex flat connections on a Riemann surface.
• In particular, the conformal TBA equations for theories in the A1 class produce solutions of the Schr\"odinger equation with a rational potential.