Dec 08, 2013
Sunday

10:40 AM  11:15 AM


Gaussian free field, random measure and KPZ on R^4
Linan Chen (McGill University)

 Location
 Evans Hall
 Video


 Abstract
 A highlight in the study of quantum physics was the work of Knizhnik, Polyakov and Zamolodchikov (1988), in which they proposed a relation (KPZ relation) between the scaling dimension of a statistical physics model in Euclidean geometry and its counterpart in the random geometry. More recently, Duplantier and Sheffield (2011) used the 2dim Gaussian free field to construct the Liouville quantum gravity measure on a planar domain, and gave the first mathematically rigorous formulation and proof of the KPZ relation in that setting. Inspired by the work of Duplantier and Sheffield, we apply a similar approach to extend their results and techniques to higher even dimensions R^(2n) for n>=2.
This talk mainly focuses on the case of R^4. I will briefly introduce the notion of Gaussian free field (GFF). In our work we adopt a specific 4dim GFF to construct a random Borel measure on R^4 which formally has the density (with respect to the Lebesgue measure) being the exponential of an instance of the GFF. Further we establish a 4dim KPZ relation corresponding to this random measure. This work is joint with Dmitry Jakobson (McGill University).
 Supplements



