Alexander Belavin - The correlation numbers in Minimal Liouville gravity
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2013-11-15

Alexander Belavin (Landau Institute et IITP, Moscou)
The correlation numbers in Minimal Liouville gravity from Douglas string equation
We continue the study of (q, p) Minimal Liouville Gravity with the help of Douglas string
equation. Generalizing the earlier results we demonstrate that there exist such
coordinates τm,n on the space of the perturbed Minimal Liouville Gravity theories, in
which the partition function of the theory is determined by the Douglas string equation.
The coordinates τm,n are related in a non-linear fashion to the natural coupling constants
λm,n of the perturbations of Minimal Liouville Gravity by the physical operators Om,n. We
find this relation from the requirement that the correlation numbers in Minimal Liouville
Gravity must satisfy the conformal and fusion selection rules.
After fixing this relation we compute three- and four-point correlation numbers when
they are not zero. The results are in agreement with direct calculations in Minimal
Liouville Gravity available in the literature.