Mathematics

Minimal Liouville Gravity (MLG)  is a theory of 2-dimensional quantum gravity or string theory in dimension d<1, it is a Conformal Field Theory which is a Minimal Model of CFT (as matter) coupled with 2d surface metric via Liouville Field Theory (after Polyakov). As in any QFT one of the main object of interest is correlators of various operator fields. Though in CFT a huge algebra of symmetries allows in principle to compute correlators, in MLG it involves complicated steps such as integration over moduli space of complex curves starting fromcorrelators of four fields. Simultaneously another approach which is believed to describe the same physical problem was developed based on matrix models. It allows to efficiently compute correlation numbers through connection to integrable hierarchies and Frobenius Manifolds. Still this matrix model computation gives slightly different result. In the talk I will talk about the results of those approaches and present some direct numerical computations of those numbers.For references one can see for example (http://lanl.arxiv.org/abs/hep-th/0510214v1, Moduli Integrals, Ground Ring and Four-Point Function inMinimal Liouville Gravity  and http://arxiv.org/abs/1310.5659).