Minimal strings and Semiclassical Expansion

TL;DR

This paper explores the relationship between minimal strings and integrable mechanical models, showing how quantum effects and brane perturbations influence the target space and wave functions.

Contribution

It establishes a novel connection between minimal string target spaces and integrable models, analyzing quantum corrections and brane effects in this framework.

Findings

Quantum effects correspond to corrections in the mechanical model.

Double scaling relates to classical turning point approximations.

ZZ brane perturbations preserve the smoothness and topology of the target space.

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.