Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity

Details Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity

1994-12-21

arxiv.org/abs/hep-th/9412176v1

Theor.Math.Phys. 104 (1996) 892-920; Teor.Mat.Fiz. 104 (1995) 158-191

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, LaTex file. Proceedings of the Vth International Conference on Mathematical Physics, Strings and Quantum gravity, Al

Scientific paper

10.1007/BF02066661

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.

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