Quantization of spectral curves and DQ-modules

TL;DR

This paper develops a framework using DQ-modules to quantize spectral curves associated with Higgs bundles and other geometric objects, unifying various quantum curve constructions.

Contribution

It introduces a novel approach linking DQ-modules to the quantization of spectral curves, broadening the understanding of quantum geometry.

Findings

Constructed DQ-modules supported on spectral curves of Higgs bundles

Established connections between DQ-modules and quantum curves in different contexts

Provided a unified framework for spectral curve quantization

Abstract

Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we construct a DQ-module supported by the spectral curve associated to this bundle. Then, we relate quantum curves arising in various situations (quantization of spectral curves of Higgs Bundles, quantization of the $A$-polynomial...) and DQ-modules and show that DQ-modules provide a suitable framework to study the quantization of spectral curves.