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].
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ArXiv ePrint: 1310.5659
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Belavin, A., Dubrovin, B. & Mukhametzhanov, B. Minimal Liouville gravity correlation numbers from Douglas string equation. J. High Energ. Phys. 2014, 156 (2014). https://doi.org/10.1007/JHEP01(2014)156
- 2D Gravity
- Conformal and W Symmetry
- Matrix Models