# Opers versus nonabelian Hodge

@article{Dumitrescu2016OpersVN, title={Opers versus nonabelian Hodge}, author={Olivia Dumitrescu and Laura Fredrickson and Georgios Kydonakis and Rafe Mazzeo and Motohico Mulase and Andrew Neitzke}, journal={arXiv: Differential Geometry}, year={2016} }

Author(s): Dumitrescu, Olivia; Fredrickson, Laura; Kydonakis, Georgios; Mazzeo, Rafe; Mulase, Motohico; Neitzke, Andrew | 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…

## 20 Citations

An invitation to 2D TQFT and quantization of Hitchin spectral curves

- Mathematics
- 2017

This article consists of two parts. In Part 1, we present a formulation of two-dimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs to the endofuntor…

From quantum curves to topological string partition functions II.

- Mathematics
- 2020

We propose a geometric characterisation of the topological string partition functions associated to the local Calabi-Yau (CY) manifolds used in the geometric engineering of $d=4$, $\mathcal{N}=2$…

Why is Landau-Ginzburg link cohomology equivalent to Khovanov homology?

- MathematicsJournal of High Energy Physics
- 2019

A bstractIn this note we make an attempt to compare a cohomological theory of Hilbert spaces of ground states in the N=22$$ \mathcal{N}=\left(2,2\right) $$ 2d Landau-Ginzburg theory in models…

Generalized B-Opers

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2020

Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper…

Interplay between Opers, Quantum Curves, WKB Analysis, and Higgs Bundles

- Mathematics
- 2017

Quantum curves were introduced in the physics literature. We develop a mathematical framework for the case associated with Hitchin spectral curves. In this context, a quantum curve is a Rees…

A journey from the Hitchin section to the
oper moduli

- MathematicsProceedings of Symposia in Pure Mathematics
- 2018

This paper provides an introduction to the mathematical notion of \emph{quantum curves}. We start with a concrete example arising from a graph enumeration problem. We then develop a theory of quantum…

Twisted cyclic quiver varieties on curves

- MathematicsEuropean Journal of Mathematics
- 2019

We study the algebraic geometry of twisted Higgs bundles of cyclic type along complex curves. These objects, which generalize ordinary cyclic Higgs bundles, can be identified with representations of…

Parabolic Higgs bundles, $tt^*$ connections and opers

- Mathematics
- 2019

The non-abelian Hodge correspondence identifies complex variations of Hodge structures with certain Higgs bundles. In this work we analyze this relationship, and some of its ramifications, when the…

Higher length-twist coordinates, generalized Heun's opers, and twisted superpotentials

- Mathematics
- 2017

In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that describes the effective twisted superpotential obtained from a class S theory geometrically as a generating function in terms…

Opers and Non-Abelian Hodge: Numerical Studies

- MathematicsExperimental Mathematics
- 2021

We present numerical experiments that test the predictions of a conjecture of Gaiotto-Moore-Neitzke and Gaiotto concerning the monodromy map for opers, the nonabelian Hodge correspondence, and the…

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