Solving Heun's equation using conformal blocks

摘要: Abstract It is known that the classical limit of second order BPZ null vector decoupling equation for simplest two 5-point degenerate spherical conformal blocks yields: (i) normal form Heun with complex accessory parameter determined by 4-point block on sphere, and (ii) a pair Floquet type linearly independent solutions. A key point in derivation above result asymptotic which so-called heavy light contributions decouple. In present work semi-classical heavy–light factorization studied. particular, mechanism responsible identified. Moreover, it shown property yields practical method computation Heun's Finally, should be stressed tools analyzed this have broad spectrum applications, studies spectral problems class potentials, sphere–torus correspondence 2d CFT, KdV theory, connection problem black hole physics. These applications are main motivations work.