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DUBROVIN’S SUPERPOTENTIAL AS A GLOBAL SPECTRAL CURVE

Part of: Quantum field theory; related classical field theories Symplectic geometry, contact geometry Deformations of analytic structures

Published online by Cambridge University Press:  17 April 2017

P. Dunin-Barkowski ,
P. Norbury ,
N. Orantin ,
A. Popolitov  and
S. Shadrin
P. Dunin-Barkowski
Affiliation:
Faculty of Mathematics, National Research University Higher School of Economics, Usacheva 6, 119048 Moscow, Russia (ptdbar@hse.ru)
P. Norbury
Affiliation:
School of Mathematics and Statistics, University of Melbourne, 3010 Australia (pnorbury@ms.unimelb.edu.au)
N. Orantin
Affiliation:
Département de mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland (nicolas.orantin@epfl.ch)
A. Popolitov
Affiliation:
Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands (A.Popolitov@uva.nl; S.Shadrin@uva.nl) ITEP, Moscow, Russia
S. Shadrin
Affiliation:
Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands (A.Popolitov@uva.nl; S.Shadrin@uva.nl)
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Abstract

We apply the spectral curve topological recursion to Dubrovin’s universal Landau–Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differentials reproduces the cohomological field theory associated with the same point of the initial Frobenius manifold.

Keywords

Frobenius manifoldGauss–Manin systemtopological recursion

MSC classification

Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory 81T45: Topological field theories
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 3 , May 2019 , pp. 449 - 497
Copyright
© Cambridge University Press 2017 

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