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

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

2005-06-20

arxiv.org/abs/hep-th/0506159v2

JHEP 0511 (2005) 049

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 6 figures

Scientific paper

10.1088/1126-6708/2005/11/049

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.

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