Non-commutative ADE geometries as holomorphic wave equations
arXiv:hep-th/0504049 · doi:10.1016/j.nuclphysb.2005.08.039
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.
17 pages, v2: version to be published
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