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Эта публикация цитируется в 19 научных статьях (всего в 19 статьях)
Minimal Liouville gravity correlation numbers from Douglas string equation
A. Belavinabc, B. Dubrovindef, B. Mukhametzhanovbg a Institute for Information Transmission Problems,
Bol’shoy karetni pereulok 19, 127994, Moscow, Russia
b L.D. Landau Institute for Theoretical Physics,
prospect academica Semenova 1a, 142432 Chernogolovka, Russia
c Moscow Institute of Physics and Technology,
Insitutsky pereulok 9, 141700 Dolgoprudny, Russia
d International School of Advanced Studies (SISSA),
Via Bonomea 265, 34136 Trieste, Italy
e N.N. Bogolyubov Laboratory for Geometrical Methods in Mathematical Physics, Moscow State University “M.V.Lomonosov”,
Leninskie Gory 1, 119899 Moscow, Russia
f V.A. Steklov Mathematical Institute,
Gubkina street 8, 119991 Moscow, Russia
g Department of Physics, Harvard University,
17 Oxford street, 02138 Cambridge, U.S.A.
Аннотация:
We continue the study of $(q, p)$ Minimal Liouville Gravity with the help of Douglas
string equation. We generalize the results of [1, 2], 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 [3–5].
Поступила в редакцию: 05.11.2013 Исправленный вариант: 16.12.2013
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