Translator Disclaimer
February 2021 From the Hitchin section to opers through nonabelian Hodge
Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis, Rafe Mazzeo, Motohico Mulase, Andrew Neitzke
Author Affiliations +
J. Differential Geom. 117(2): 223-253 (February 2021). DOI: 10.4310/jdg/1612975016

Abstract

For a complex simple simply connected Lie group $G$, and a compact Riemann surface $C$, we consider two sorts of families of flat $G$-connections over $C$. Each family is determined by a point $\mathbf{u}$ of the base of Hitchin’s integrable system for $(G,C)$. One family $\nabla_{\hbar ,\mathbf{u}}$ consists of $G$-opers, and depends on $\hbar \in \mathbb{C}^\times$. The other family $\nabla_{R, \zeta,\mathbf{u}}$ is built from solutions of Hitchin’s equations, and depends on $\zeta \in \mathbb{C}^\times , R \in \mathbb{R}^+$. We show that in the scaling limit $R \to 0, \zeta = \hbar R$, we have $\nabla_{R,\zeta,\mathbf{u}} \to \nabla_{\hbar,\mathbf{u}}$. This establishes and generalizes a conjecture formulated by Gaiotto.

Citation

Download Citation

Olivia Dumitrescu. Laura Fredrickson. Georgios Kydonakis. Rafe Mazzeo. Motohico Mulase. Andrew Neitzke. "From the Hitchin section to opers through nonabelian Hodge." J. Differential Geom. 117 (2) 223 - 253, February 2021. https://doi.org/10.4310/jdg/1612975016

Information

Received: 5 September 2017; Published: February 2021
First available in Project Euclid: 10 February 2021

Digital Object Identifier: 10.4310/jdg/1612975016

Subjects:
Primary: 53C07, 58E15
Secondary: 14D21, 81T13

Rights: Copyright © 2021 Lehigh University

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.117 • No. 2 • February 2021
Back to Top