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TMF, 2016, Volume 189, Number 3, Pages 429–445 (Mi tmf9219)  

This article is cited in 2 scientific papers (total in 2 papers)

Flat coordinates for Saito Frobenius manifolds and string theory.

A. A. Belavinabc, D. Gepnerd, Ya. A. Kononovce

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia
b Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia
c Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow region, Russia
d Department of Particle Physics and Astrophysics, Faculty of Physics, Weizmann Institute of Science, Rehovot, Israel
e National Research University "Higher School of Economics" Moscow, Russia

Abstract: We investigate the connection between the models of topological conformal theory and noncritical string theory with Saito Frobenius manifolds. For this, we propose a new direct way to calculate the flat coordinates using the integral representation for solutions of the Gauss–Manin system connected with a given Saito Frobenius manifold. We present explicit calculations in the case of a singularity of type $A_n$. We also discuss a possible generalization of our proposed approach to $SU(N)_k/(SU(N)_{k+1} \times U(1))$ Kazama–Suzuki theories. We prove a theorem that the potential connected with these models is an isolated singularity, which is a condition for the Frobenius manifold structure to emerge on its deformation manifold. This fact allows using the Dijkgraaf–Verlinde–Verlinde approach to solve similar Kazama–Suzuki models.

Keywords: Frobenius manifold, flat coordinates, string theory

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
The research of A. A. Belavin was performed at the Institute for Information Transmission Problems, RAS, and supported by a grant from the Russian Science Foundation (Project No. 14-50-00150).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9219

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English version:
Theoretical and Mathematical Physics, 2016, 189:3, 1775–1789

Bibliographic databases:

Received: 07.05.2016

Citation: A. A. Belavin, D. Gepner, Ya. A. Kononov, “Flat coordinates for Saito Frobenius manifolds and string theory.”, TMF, 189:3 (2016), 429–445; Theoret. and Math. Phys., 189:3 (2016), 1775–1789

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. Aleshkin, A. Belavin, “A new approach for computing the geometry of the moduli spaces for a Calabi–Yau manifold”, J. Phys. A-Math. Theor., 51:5 (2018), 055403  crossref  mathscinet  zmath  isi  scopus
    2. K. Aleshkin, A. Belavin, “Special geometry on the moduli space for the two-moduli non-Fermat Calabi–Yau”, Phys. Lett. B, 776 (2018), 139–144  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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