Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk

Konstantin Aleshkin, Vladimir Belavin, Chaiho Rim

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


There are two alternative approaches to the minimal gravity — direct Liouville approach and matrix models. Recently there has been a certain progress in the matrix model approach, growing out of presence of a Frobenius manifold (FM) structure embedded in the theory. The previous studies were mainly focused on the spherical topology. Essentially, it was shown that the action principle of Douglas equation allows to define the free energy and to compute the correlation numbers if the resonance transformations are properly incorporated. The FM structure allows to find the explicit form of the resonance transformation as well as the closed expression for the partition function. In this paper we elaborate on the case of gravitating disk. We focus on the bulk correlators and show that in the similar way as in the closed topology the generating function can be formulated using the set of flat coordinates on the corresponding FM. Moreover, the resonance transformations, which follow from the spherical topology consideration, are exactly those needed to reproduce FZZ result of the Liouville gravity approach.

Original languageEnglish
Article number169
JournalJournal of High Energy Physics
Issue number11
StatePublished - 1 Nov 2017
Externally publishedYes


  • 2D Gravity
  • Conformal Field Theory
  • Matrix Models
  • Nonperturbative Effects


Dive into the research topics of 'Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk'. Together they form a unique fingerprint.

Cite this