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 τ 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 τ m,n are related in a non-linear fashion to the natural coupling constants λ 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]. © 2014 The Author(s).

Minimal Liouville gravity correlation numbers from Douglas string equation / Belavin, A.; Dubrovin, Boris; Mukhametzhanov, B.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2014:1(2014), pp. 1-50. [10.1007/JHEP01(2014)156]

Minimal Liouville gravity correlation numbers from Douglas string equation

Dubrovin, Boris;
2014-01-01

Abstract

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 τ 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 τ m,n are related in a non-linear fashion to the natural coupling constants λ 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]. © 2014 The Author(s).
2014
2014
1
1
50
A156
10.1007/JHEP01(2014)156
https://arxiv.org/abs/1310.5659
http://cdsads.u-strasbg.fr/abs/2014JHEP...01..156B
Belavin, A.; Dubrovin, Boris; Mukhametzhanov, B.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/17074
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