Noncommutative (super) p-branes and Moyal-Yang star products with a lower and upper scale

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.