Quantum gravity and the KPZ formula [after Duplantier-Sheffield]. (English) Zbl 1295.83034
Séminaire Bourbaki. Volume 2011/2012. Exposés 1043–1058. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-371-3/pbk). Astérisque 352, 315-354, Exp. No. 1052 (2013).
The Knizhik, Polyakov and Zamolodchikov (KPZ) formula relates statistical mechanical models in two dimensions with quantum gravity models. The nature and origin of the formula remained mysterious for some time, being rigorously a conjecture rather than a formula. This paper describes how recent work of Duplantier and Sheffield clarifies some of the mystery behind the formula, through the uniformization of the random lattices involved when seen as a Riemann surface.
For the entire collection see [Zbl 1275.00032].
For the entire collection see [Zbl 1275.00032].
Reviewer: Jorge Pullin (Baton Rouge)
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 60G15 | Gaussian processes |
| 60K40 | Other physical applications of random processes |
| 81V17 | Gravitational interaction in quantum theory |
| 83C45 | Quantization of the gravitational field |
