Noncommutative D-brane and open string in pp-wave background with B-field

The open string ending on a D-brane with a constant B-field in a pp-wave Ramond-Ramond background is exactly solvable. The theory is controlled by three dimensionful parameters: alpha', the mass parameter (RR background times the lightcone momentum) and the B-field. We quantize the open string theory and determine the full noncommutative structure, In particular, we find a fully noncommutative phase space whose noncommutativity depends on all these parameters. The lightcone Hamiltonian is obtained, and as a consequence of the nontrivial commutation relations of the theory, new features of the spectrum are noted. Various scaling limits of the string results are considered. Physical implications are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.