Gauge Theories in Noncommutative Homogeneous Kähler Manifolds

Abstract

We construct a gauge theory on a noncommutative homogeneous Kähler manifold, where we employ the deformation quantization with separation of variables for Kähler manifolds formulated by Karabegov. A key point in this construction is to obtaining vector fields which act as inner derivations for the deformation quantization. We show that these vector fields are the only Killing vector fields. We give an explicit construction of this gauge theory on noncommutative $\mathbb{C}{P}^N$ and noncommutative $\mathbb{C}{H}^N$.

27 pages, typos corrected

References in corpus (5)

• Large N reduction on group manifolds
• An explicit formula for a star product with separation of variables
• Large N reduction on coset spaces
• Are Vortex Numbers Preserved?
• Explicit Formulae for Noncommutative Deformations of CP^N and CH^N

Cited by in corpus (2)

• Contravariant geometry and emergent gravity from noncommutative gauge theories
• Explicit formula of deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold