Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings

Abstract

The target space $M_{p,q}$ of $(p,q)$ minimal strings is embedded into the phase space of an associated integrable classical mechanical model. This map is derived from the matrix model representation of minimal strings. Quantum effects on the target space are obtained from the semiclassical mechanics in phase space as described by the Wigner function. In the classical limit the target space is a fold catastrophe of the Wigner function that is smoothed out by quantum effects. Double scaling limit is obtained by resolving the singularity of the Wigner function. The quantization rules for backgrounds with ZZ branes are also derived.

16 pages, 6 figures

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Cited by in corpus (5)

• The Library of Babel: On the origin of gravitational thermodynamics
• The emergence of noncommutative target space in noncritical string theory
• Quantum curves as quantum distributions
• Geometric Transition as a Change of Polarization
• Minimal strings and Semiclassical Expansion