%0 Journal Article
%D 2014
%T Minimal Liouville gravity correlation numbers from Douglas string equation
%A Alexander Belavin
%A Boris Dubrovin
%A Baur Mukhametzhanov
%X We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \cite{Moore:1991ir}, \cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that there exist such coordinates $\tau_{m,n}$ 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 $\tau_{m,n}$ are related in a non-linear fashion to the natural coupling constants $\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the physical operators $O_{m,n}$. 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 the direct calculations in Minimal Liouville Gravity available in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj}, \cite{Belavin:2006ex}.
%I Springer
%G en
%U http://urania.sissa.it/xmlui/handle/1963/34588
%1 34795
%2 Physics
%4 2
%$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T14:45:32Z
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%R 10.1007/JHEP01(2014)156