Minimal strings and Semiclassical Expansion

Abstract

The target space of minimal $(2,2m-1)$ strings is embedded into the phase space of an integrable mechanical model. Quantum effects on the target space correspond to quantum corrections on the mechanical model. In particular double scaling is equivalent to standard uniform approximation at the classical turning points ot the mechanical model. After adding ZZ brane perturbations the quantum target remains smooth and topologically trivial. Around the ZZ brane singularities the Baker-Ahkiezer wave function is given in terms of the parabollic cylinder function.