Journal of High Energy Physics

, 2014:156 | Cite as

Minimal Liouville gravity correlation numbers from Douglas string equation

  • Alexander Belavin
  • Boris Dubrovin
  • Baur MukhametzhanovEmail author
Open Access


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, 4, 5].


2D Gravity Conformal and W Symmetry Matrix Models 


Open Access

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Alexander Belavin
    • 1
    • 2
    • 3
  • Boris Dubrovin
    • 4
    • 5
    • 6
  • Baur Mukhametzhanov
    • 1
    • 7
    Email author
  1. 1.L.D.Landau Institute for Theoretical Physicsprospect academica Semenova 1aChernogolovkaRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Institute for Information Transmission ProblemsMoscowRussia
  4. 4.International School of Advanced Studies (SISSA)TriesteItaly
  5. 5.N.N. Bogolyubov Laboratory for Geometrical Methods in Mathematical PhysicsMoscow State University “M.V.Lomonosov”MoscowRussia
  6. 6.V.A. Steklov Mathematical InstituteMoscowRussia
  7. 7.Department of PhysicsHarvard UniversityCambridgeU.S.A.

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