Noncommutative Solitons and Intersecting D-Branes

Brane configurations that contain a tachyonic mode are unstable and will decay. The decay modes vary depending on the unstable D-brane configurations involved ~see the reviews @1–3#!. In bosonic string theory, all D-branes are unstable. The tachyon on the brane may condense to solitonic solutions of the open string tachyon field theory. These solitons have been noted to correspond to lower dimensional unstable D-branes @4,5#. In type II super-strings, there are stable tachyon vortex solutions arising from DD̄-brane annihilation @6,7# corresponding to codimension-2 stable Bogomol’nyi-Prasad-Sommerfield ~BPS! D-branes. It was noticed @8,9# that the construction of solitonic D-brane solutions is remarkably simplified in the presence of an infinite nonzero B field. The tachyon field theory becomes noncommutative and, using the operator formalism, the D-brane solutions, now noncommutative ~NC! solitons @10#, are easily constructed. These NC solitonic D-brane solutions have since been improved to allow for an arbitrary nonzero finite B field @11#. In this paper, we present new decay modes of unstable brane configurations in the presence of a nonzero B field. Our aim is to construct decay modes within the context of the NC operator formalism corresponding to intersecting brane configurations. The intersecting branes we construct all have a nonzero B field in their world volume. In Sec. II, we carry this out within the context of bosonic string theory, using as a specific example the decay of unstable D25-branes. We find that configurations of two intersecting D(p22)-branes can be constructed only from the decay of two or more Dp-branes. Starting from one Dp-brane, one can obtain perpendicular brane configurations consisting of D(p24)-branes plus defect D(p22)-branes. Defect branes are D-branes containing bubbles of the closed string vacuum. The defect Dp-brane soliton is time independent and asymptotically approaches the solution of the Dp-brane. We conclude the section by constructing nonperpendicularly intersecting D-branes. In Sec. III, we extend our results to the type II superstrings. Special to the superstring case is that perpendicularly intersecting brane configurations can be constructed from the decay of a single Dp-D̄p system. In particular, it is possible