Non-𝒜belian Geometry |
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Authors: | Keshav Dasgupta Zheng Yin |
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Institution: | (1) School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA. E-mail: keshav@sns.ias.edu; yin@sns.ias.edu, US |
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Abstract: | Spatial noncommutativity is similar and can even be related to the non- Abelian nature of multiple D-branes. But they have
so far seemed independent of each other. Reflecting this decoupling, the algebra of matrix valued fields on noncommutative
space is thought to be the simple tensor product of constant matrix algebra and the Moyal-Weyl deformation. We propose scenarios
in which the two become intertwined and inseparable. Therefore the usual separation of ordinary or noncommutative space from
the internal discrete space responsible for non-Abelian symmetry is really the exceptional case of an unified structure. We
call it non-Abelian geometry. This general structure emerges when multiple D-branes are configured suitably in a flat but varying B field background, or in the presence of non-Abelian gauge field background. It can also occur in connection with Taub-NUT
geometry. We compute the deformed product of matrix valued functions using the lattice string quantum mechanical model developed
earlier. The result is a new type of associative algebra defining non-Abelian geometry. A possible supergravity dual is also
discussed.
Received: 13 December 2000 / Accepted: 24 October 2002 Published online: 24 January 2003
Communicated by R. H. Dijkgraaf |
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