Abstract
We discuss how to formulate the matrix model actions describing the multiple D-brane dynamics on curved (Kähler) manifolds along the lines of [1], [2]. We briefly review the D-geometry axioms, the requirement that the action reproduce the masses of stretched open strings. In the case of three complex dimensions we show that the axioms cannot be satisfied unless the metric is Ricci flat, and argue that such actions do exist when the metric is Ricci flat. The results provide a noncommutative extension of Kähler geometry.
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Kato, A. (2001). D-Brane Actions on Kähler Manifolds. In: Maeda, Y., Moriyoshi, H., Omori, H., Sternheimer, D., Tate, T., Watamura, S. (eds) Noncommutative Differential Geometry and Its Applications to Physics. Mathematical Physics Studies, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0704-7_6
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DOI: https://doi.org/10.1007/978-94-010-0704-7_6
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