Non-commutative ADE geometries as holomorphic wave equations

Details Non-commutative ADE geometries as holomorphic wave equations Non-commutative ADE geometries as holomorphic wave equations

2005-04-06

arxiv.org/abs/hep-th/0504049v2

Nucl.Phys. B727 (2005) 499-512

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, v2: version to be published

Scientific paper

10.1016/j.nuclphysb.2005.08.039

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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