Minimal Liouville gravity correlation numbers from Douglas string equation
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, 2 s + 1) was studied, to (3, 3 s + 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].
- Publication:
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Journal of High Energy Physics
- Pub Date:
- January 2014
- DOI:
- 10.1007/JHEP01(2014)156
- arXiv:
- arXiv:1310.5659
- Bibcode:
- 2014JHEP...01..156B
- Keywords:
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- 2D Gravity;
- Conformal and W Symmetry;
- Matrix Models;
- High Energy Physics - Theory
- E-Print:
- 58 pages