Journal article

DUBROVIN'S SUPERPOTENTIAL AS A GLOBAL SPECTRAL CURVE

P Dunin-Barkowski, P Norbury, N Orantin, A Popolitov, S Shadrin

Journal of the Institute of Mathematics of Jussieu | CAMBRIDGE UNIV PRESS | Published : 2019

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.

University of Melbourne Researchers

Grants

Awarded by RFBR


Awarded by RFBR-India


Funding Acknowledgements

We thank Todor Milanov for useful discussions and Boris Dubrovin for suggesting the connection between superpotentials and topological recursion. A. P. and S. S. were supported by a Vici grant of the Netherlands Organization for Scientific research. P.D.-B. was partially supported by RFBR grants 16-31-60044-mol-a-dk, 15-01-05990, 15-31-20832-mol-a-ved and 15-52-50041-YaF-a and RFBR-India grant 14-01-92691-Ind-a; A. P. was partially supported by RFBR grants 13-02-00457, 14-01-31492-mol-a, 15-52-50041-YaF-a and 15-31-20832-mol-a-ved. P. D.-B. was also partially supported by the Government of the Russian Federation within the framework of a subsidy granted to the National Research University Higher School of Economics for the implementation of the Global Competitiveness Program and by an MPIM Bonn fellowship.