MENU

You are here

Minimal Liouville gravity correlation numbers from Douglas string equation

TitleMinimal Liouville gravity correlation numbers from Douglas string equation
Publication TypeJournal Article
Year of Publication2014
AuthorsBelavin, A, Dubrovin, B, Mukhametzhanov, B
Abstract

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}.

URLhttp://urania.sissa.it/xmlui/handle/1963/34588
DOI10.1007/JHEP01(2014)156

Sign in