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: α′, 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