Quantum Gravity and String Theory


Noncommutative (Super) P-Branes and Moyal-Yang Star Products with a Lower and Upper Scale

Authors: Carlos Castro

Noncommutative p-brane actions, for even p+1 = 2n-dimensional world-volumes, are written explicitly in terms of the novel Moyal-Yang ( Fedosov-Kontsevich ) star product deformations of the Noncommutative Nambu Poisson Brackets (NCNPB) that are associated with the noncommuting world-volume coordinates qA, pA for A = 1, 2, 3, ...n. The latter noncommuting coordinates obey the noncommutative Yang algebra with an ultraviolet LP (Planck) scale and infrared (R ) scale cutoff. It is shown why our p-brane actions in the "classical" limit ℏeff = ℏLP/R → 0 still acquire nontrivial noncommutative corrections that differ from ordinary p-brane actions. Super p-branes actions in the light-cone gauge are also amenable to Moyal-Yang star product deformations as well due to the fact that p-branes moving in flat spacetime backgrounds, in the light-cone gauge, can be recast as gauge theories of volume-preserving diffeomorphisms. The most general construction of noncommutative super p-branes actions based on non ( anti ) commuting superspaces and quantum group methods remains an open problem.

Comments: 8 pages, This article appeared in Phys. Letts B 626 (2005) 209.

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[v1] 26 Aug 2009

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