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

  title={Interplay between Opers, Quantum Curves, WKB Analysis, and Higgs Bundles},
  author={Olivia Dumitrescu and Motohico Mulase},
  journal={arXiv: Algebraic Geometry},
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 $\mathcal{D}$-module on a smooth projective algebraic curve, whose semi-classical limit produces the Hitchin spectral curve of a Higgs bundle. We give a method of quantization of Hitchin spectral curves by concretely constructing one-parameter deformation families of opers. We propose a generalization of… 

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