Intersecting D-Branes in ten and six dimensions
Klaus Behrndt, Eric Bergshoeff, Bert Janssen
TL;DR
The paper presents a systematic framework for constructing intersecting D-brane configurations in ten and six dimensions using T-duality, by embedding Type IIB branes into higher-dimensional nine- and five-branes and classifying the resulting intersections. It shows that only a constrained subclass of these intersections satisfies the IIA/IIB supergravity equations of motion, with d=10 branes described by a single harmonic function and d=6 branes by two harmonic functions, interpretable as intersections of two 10d branes. The authors also connect these ten-dimensional constructions to six-dimensional branes via K3 compactification and employ string/string/string triality to relate to heterotic NS/NS string and five-brane intersections, providing a cohesive picture across dimensions. Overall, the work clarifies how brane intersections encode lower-dimensional physics and offers a path to analyzing related black hole solutions and heterotic duals within a unified brane-intersection framework.
Abstract
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/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.