Intersecting D-branes in ten and six dimensions

We show how, via T duality, intersecting D brane configurations in ten (six) dimensions can be obtained from the elementary D-brane configurations by embedding a type IIB D-brane into a type IIB nine-brane (five-brane) and give a classification of such configurations. We show that only a very specific subclass of these configurations can be realized as (supersymmetric) solutions to the equations of motion of IIA or IIB supergravity. Whereas the elementary D-brane solutions in d=10 are characterized by a single harmonic function, those in d=6 contain two independent harmonic functions and may be viewed as the intersection of two d=10 elementary D-branes. Using string-string-string triality in six dimensions we show that the heterotic version of the elementary d=6 D-brane solutions correspond in ten dimensions to intersecting Neveu-Schwarz-Neveu-Schwarz (NS-NS) strings or five-branes and their T duals. We comment on the implications of our results in other than ten and six dimensions.