Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 8

Special Kähler geometry of the Hitchin system and topological recursion

Pages: 1981 – 2024

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n8.a2

Authors

David Baraglia (School of Mathematical Sciences, University of Adelaide, SA, Australia)

Zhenxi Huang (School of Mathematical Sciences, University of Adelaide, SA, Australia)

Abstract

We investigate the special Kähler geometry of the base of the Hitchin integrable system in terms of spectral curves and topological recursion. The Taylor expansion of the special Kähler metric about any point in the base may be computed by integrating the $g = 0$ Eynard–Orantin invariants of the corresponding spectral curve over cycles. In particular, we show that the Donagi–Markman cubic is computed by the invariant $W^{(0)}_3$. We use topological recursion to go one step beyond this and compute the symmetric quartic of second derivatives of the period matrix.