TY - JOUR

T1 - Minimal gravity and Frobenius manifolds

T2 - bulk correlation on sphere and disk

AU - Aleshkin, Konstantin

AU - Belavin, Vladimir

AU - Rim, Chaiho

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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.

AB - 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.

KW - 2D Gravity

KW - Conformal Field Theory

KW - Matrix Models

KW - Nonperturbative Effects

UR - http://www.scopus.com/inward/record.url?scp=85036621032&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2017)169

DO - 10.1007/JHEP11(2017)169

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AN - SCOPUS:85036621032

SN - 1126-6708

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 11

M1 - 169

ER -