2025/10/28 by Ma, Chen-Te · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2510.24998
We examine the role of non-commutative geometry in Dp-branes within large R-R field backgrounds. In this context, the background of a significant (p-1)-form R-R field can be effectively described using a (p-1)-bracket, similar to the method used in the NS-NS case. We begin by recalling how non-commutative geometry arises from the quantization of open string theory. In this framework, the Seiberg-Witten map is a key element that establishes the equivalence between commutative and non-commutative descriptions in the low-energy effective theory. The Poisson bracket characterizes non-commutative structures, with deformation achieved through the Moyal product. Next, we show how the Nambu-Poisson bracket emerges in the context of a single D4-brane with the large R-R field background limit, starting from the BLG model. The generalization to a Dp-brane leads to the (p-1)-bracket description, which reveals a duality web relating NS-NS and R-R field backgrounds via T-duality and S-duality in the low-energy limit. Finally, we extend the single D-brane construction to multiple D-branes by promoting the ordinary product in the bracket to a covariant derivative at the Poisson level.