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Flat coordinates for Saito Frobenius manifolds and string theory

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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 × 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.

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Author information

Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia

    A. A. Belavin & Ya. A. Kononov

  2. Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

    A. A. Belavin

  3. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia

    A. A. Belavin

  4. Department of Particle Physics, Weizmann Institute, Rehovot, Israel

    D. Gepner

  5. National Research University Higher School of Economics, Moscow, Russia

    Ya. A. Kononov

Authors
  1. A. A. Belavin
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  2. D. Gepner
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  3. Ya. A. Kononov
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Corresponding author

Correspondence to A. A. Belavin.

Additional information

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).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 189, No. 3, pp. 429–445, December, 2016.

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Belavin, A.A., Gepner, D. & Kononov, Y.A. Flat coordinates for Saito Frobenius manifolds and string theory. Theor Math Phys 189, 1775–1789 (2016). https://doi.org/10.1134/S0040577916120096

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