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arXiv · 1403.5727

Gauge Theories in Noncommutative Homogeneous Kähler Manifolds

Yoshiaki Maeda·Akifumi Sako·Toshiya Suzuki·Hiroshi Umetsu
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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 ${\mathbb C}H^N$.

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Yoshiaki Maeda, Akifumi Sako, Toshiya Suzuki, Hiroshi Umetsu. 2014-09-07. Gauge Theories in Noncommutative Homogeneous Kähler Manifolds. https://doi.org/10.1063/1.4893982

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