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Duality and the Knizhnik-Polyakov-Zamolodchikov relation in Liouville quantum gravity
Bertrand Duplantier1, Scott Sheffield
1Institut de Physique Théorique, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France.
Abstract:
We present a (mathematically rigorous) probabilistic and geometrical proof of the Knizhnik-Polyakov-Zamolodchikov relation between scaling exponents in a Euclidean planar domain D and in Liouville quantum gravity. It uses the properly regularized quantum area measure dmicro_{gamma}=epsilon;{gamma;{2}/2}e;{gammah_{epsilon}(z)}dz, where dz is the Lebesgue measure on D, gamma is a real parameter, 0
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