Noncommutative D-brane and Open String in pp-wave Background with B-field

TL;DR

This paper shows that an open string ending on a D-brane in a pp-wave background with a constant B-field exhibits a rich noncommutative structure that involves both coordinates and momenta, with the noncommutativity explicitly depending on the mass parameter m and the light-cone momentum p+. The authors derive the complete open string mode expansion, compute the symplectic form, and obtain a set of commutation relations in which the zero modes and the boundary endpoints become noncommutative. They also analyze scaling limits, recovering Seiberg-Witten type noncommutativity in the small B limit and revealing a deformed fully noncommutative phase space when m is nonzero in the large B limit. The results imply a probe dependent phase space and offer avenues for defining corresponding noncommutative field theories in pp-wave backgrounds, with potential implications for string dualities and quantum geometry.

Abstract

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 Hamiltionian 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.