Counts of (tropical) curves in and Feynman integrals

  • Janko Böhm

    Kaiserslautern University, Germany
  • Christoph Goldner

    Eberhard Karls University Tübingen, Germany
  • Hannah Markwig

    Eberhard Karls University Tübingen, Germany
Counts of (tropical) curves in $E \times \mathbb{P}^1$ and Feynman integrals cover
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Abstract

We study generating series of Gromov–Witten invariants of and their tropical counterparts. Using tropical degeneration and floor diagram techniques, we can express the generating series as sums of Feynman integrals, where each summand corresponds to a certain type of graph which we call a . The individual summands are – just as in the case of mirror symmetry of elliptic curves, where the generating series of Hurwitz numbers equals a sum of Feynman integrals – complex analytic path integrals involving a product of propagators (equal to the Weierstrass--function plus an Eisenstein series). We also use pearl chains to study generating functions of counts of tropical curves in of so-called \textit{leaky degree}.

Cite this article

Janko Böhm, Christoph Goldner, Hannah Markwig, Counts of (tropical) curves in and Feynman integrals. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 9 (2022), no. 1, pp. 121–158

DOI 10.4171/AIHPD/115