Non-commutative ADE geometries as holomorphic wave equations
Adil Belhaj, Jorgen Rasmussen, El Hassan Saidi, Abdellah Sebbar
TL;DR
This paper introduces a non-commutative framework for ADE geometries in Calabi-Yau manifolds, deriving holomorphic wave equations and analyzing their spectra as quantum moduli spaces, with detailed study of quantum A_1 geometry.
Contribution
It presents a novel non-commutative approach to ADE geometries, deriving associated holomorphic wave equations and exploring their spectra as quantum moduli spaces.
Findings
Holomorphic wave equations derived for non-commutative ADE geometries
Spectrum interpreted as quantum moduli space
Quantum A_1 geometry linked to Whittaker differential equation
Abstract
Borrowing ideas from the relation between classical and quantum mechanics, we study a non-commutative elevation of the ADE geometries involved in building Calabi-Yau manifolds. We derive the corresponding geometric hamiltonians and the holomorphic wave equations representing these non-commutative geometries. The spectrum of the holomorphic waves is interpreted as the quantum moduli space. Quantum A_1 geometry is analyzed in some details and is found to be linked to the Whittaker differential equation.
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