2d Cft/Gauge/Bethe Correspondence And Solvable Quantum Mechanical Systems

The holomorphic accessory parameters for the Heun (Fuchs with four singularities) and the Lame equations are obtained by taking the classical limit of some null vector decoupling equations appearing in two-dimensional conformal field theory. In addition, a link between the aforementioned accessory parameters and the solution of some Bethe-like equations which occur in the supersymmetric gauge theories, is established.