Duality in Liouville Theory as a Reduced Symmetry

Details Duality in Liouville Theory as a Reduced Symmetry Duality in Liouville Theory as a Reduced Symmetry

1999-06-15

arxiv.org/abs/hep-th/9906116v1

Phys.Lett. B461 (1999) 66-70

Physics

High Energy Physics

High Energy Physics - Theory

Plain TeX file; 9 pages

Scientific paper

10.1016/S0370-2693(99)00816-3

The origin of the rather mysterious duality symmetry found in quantum Liouville theory is investigated by considering the Liouville theory as the reduction of a WZW-like theory in which the form of the potential for the Cartan field is not fixed a priori. It is shown that in the classical theory conformal invariance places no condition on the form of the potential, but the conformal invariance of the classical reduction requires that it be an exponential. In contrast, the quantum theory requires that, even before reduction, the potential be a sum of two exponentials. The duality of these two exponentials is the fore-runner of the Liouville duality. An interpretation for the reflection symmetry found in quantum Liouville theory is also obtained along similar lines.

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