Skip to main content


  • P. Dunin-Barkowski (a1), P. Norbury (a2), N. Orantin (a3), A. Popolitov (a4) (a5) and S. Shadrin (a4)...

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.

Hide All
1. Alexandrov, A., Mironov, A. and Morozov, A., Partition functions of matrix models: first special functions of string theory, Internat. J. Modern Phys. A 19(24) (2004), 41274163.
2. Andersen, J., Chekhov, L., Norbury, P. and Penner, R., Models of discretized moduli spaces, cohomological field theories, and Gaussian means, J. Geom. Phys. 98 (2015), 312329.
3. Bouchard, V. and Eynard, B., Think globally, compute locally, JHEP(02) (2013), 143, 34pp.
4. Bouchard, V. and Eynard, B., Private communication.
5. Do, N. and Manescu, D., Quantum curves for the enumeration of ribbon graphs and hypermaps, Commun. Number Theory Phys. 8(4) (2014), 677701.
6. Dubrovin, B., Geometry of 2D topological field theories, in Integrable Systems and Quantum Groups (Authors: R. Donagi, B. Dubrovin, E. Frenkel, E. Previato) (ed. Francaviglia, M. and Greco, S.), Springer Lecture Notes in Mathematics, 1620, pp. 120348 (Springer, Berlin, 1996).
7. Dubrovin, B., Painlevé transcendents and two-dimensional topological field theory, in The Painlevé Property: One Century Later (ed. Conte, R.), pp. 287412 (Springer, New York, 1999).
8. Dubrovin, B., On almost duality for Frobenius manifolds, in Geometry, Topology, and Mathematical Physics, American Mathematical Society Translation Series 2, 212, pp. 75132 (American Mathematical Society, Providence, RI, 2004).
9. Dumitrescu, O., Mulase, M., Safnuk, B. and Sorkin, A., The spectral curve of the Eynard–Orantin recursion via the Laplace transform, in Algebraic and Geometric Aspects of Integrable Systems and Random Matrices (ed. Dzhamay, Maruno and Pierce), Contemporary Mathematics, 593, pp. 263315 (Amer. Math. Soc., Providence, RI, 2013).
10. Dunin-Barkowski, P., Orantin, N., Shadrin, S. and Spitz, L., Identification of the Givental formula with the spectral curve topological recursion procedure, Commun. Math. Phys. 328 (2014), 669700.
11. Dunin-Barkowski, P., Orantin, N., Popolitov, A. and Shadrin, S., Combinatorics of loop equations for branched covers of sphere, preprint, 2014, arXiv:1412.1698.
12. Dunin-Barkowski, P., Lewanski, D., Popolitov, A. and Shadrin, S., Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson–Pandharipande–Tseng formula, preprint, 2015, arXiv:1504.07440.
13. Dunin-Barkowski, P., Shadrin, S. and Spitz, L., Givental graphs and inversion symmetry, Lett. Math. Phys. 103(5) (2013), 533557.
14. Eynard, B., Invariants of spectral curves and intersection theory of moduli spaces of complex curves, Commun. Number Theory Phys. 8(3) (2014), 541588.
15. Eynard, B., A short overview of the ‘Topological recursion’, preprint, 2014,arXiv:1412.3286.
16. Eynard, B. and Orantin, N., Invariants of algebraic curves and topological expansion, Commun. Number Theory Phys. 1(2) (2007), 347452.
17. Eynard, B. and Orantin, N., Topological recursion in enumerative geometry and random matrices, J. Phys. A: Math. Theor. 42 (2009), 293001 (117pp).
18. Faber, C., Shadrin, S. and Zvonkine, D., Tautological relations and the r-spin Witten conjecture, Ann. Sci. Éc. Norm. Supér. (4) 43(4) (2010), 621658.
19. Fang, B., Liu, C.-C. M. and Zong, Z., The Eynard–Orantin recursion and equivariant mirror symmetry for the projective line, Geom. Topol. to appear arXiv:1411.3557.
20. Frobenius, G. and Stickelberger, L., Über die Differentiation der elliptischen Functionen nach den Perioden und Invarianten, J. Reine Angew. Math. 92 (1882), 311327.
21. Givental, A., Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1(4) (2001), 551568.
22. Givental, A., A n-1 singularities and n-KdV hierarchies, Mosc. Math. J. 3(2) (2003), 475505.
23. Kontsevich, M. and Manin, Y., Gromov–Witten classes, quantum cohomology, and enumerative geometry, Commun. Math. Phys. 164(3) (1994), 525562.
24. Lewanski, D., Popolitov, A., Shadrin, S. and Zvonkine, D., Chiodo formulas for the -th roots and topological recursion, preprint, 2015, arXiv:1504.07439.
25. Milanov, T., The Eynard–Orantin recursion for the total ancestor potential, Duke Math. J. 163(9) (2014), 17951824.
26. Milanov, T., The Eynard–Orantin recursion for simple singularities, Commun. Number Theory Phys. 9 (2015), 707739.
27. Norbury, P., Counting lattice points in the moduli space of curves, Math. Res. Lett. 17 (2010), 467481.
28. Pandharipande, R., Pixton, A. and Zvonkine, D., Relations on M g, n via 3-spin structures, J. Amer. Math. Soc. 28(1) (2015), 279309.
29. Shadrin, S., BCOV theory via Givental group action on cohomological field theories, Mosc. Math. J. 9(2) (2009), 411429.
30. Teleman, C., The structure of 2D semi-simple field theories, Invent. Math. 188(3) 525588.
31. Witten, E., Algebraic geometry associated with matrix models of two-dimensional gravity, in Topological Methods in Modern Mathematics (Stony Brook, NY, 1991), pp. 235269 (Publish or Perish, Houston, TX, 1993).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 22 *
Loading metrics...

Abstract views

Total abstract views: 177 *
Loading metrics...

* Views captured on Cambridge Core between 17th April 2017 - 16th August 2018. This data will be updated every 24 hours.