Large Strebel graphs and $(3,2)$ Liouville CFT

Severin Charbonnier

IPhT

Mon, Oct. 09th 2017, 11:00-12:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

2D quantum gravity is the idea that a set of discretized surfaces (called map, a graph on a surface), equipped with a graph measure, converges in the large size limit (large number of faces) to a conformal field theory (CFT), and in the simplest case to the simplest CFT known as pure gravity, also known as the gravity dressed $(3,2)$ minimal model. \par Planar Strebel graphs are linked to the Strebel foliation of the moduli space of genus 0 Riemann surfaces with n punctures. Restricting this set to graphs which have the same perimeter on every face, makes all computations explicit afterward. We also define the observables to be computed, and their encoding in generating functions. \par I will then define the spectral curve of this model, which --by the means of Topological Recursion-- allows to compute all the observables. It is computable explicitly thanks to the knowledge of intersection numbers of genus 0. \par In the end, by tuning the parameters of the model, we show how to reach a critical point. At this point, the behaviour of observables of large graphs is accessible. We show that at the critical point, the spectral curve is equivalent to the one of the $(3,2)$ minimal model in CFT. This new result is a strong hint that large Strebel graphs shall be equivalent to the the gravity dressed $(3,2)$ minimal model.

Contact : Vincent
PASQUIER