Intersection Rules for p-Branes

TL;DR

This paper derives a universal, model-independent rule for how extremal p-branes intersect in various dimensions, compatible with supersymmetry, and applicable to string theory and M-theory branes.

Contribution

It introduces a general, derivation-based intersection rule for extremal branes in arbitrary dimensions, independent of supersymmetry assumptions.

Findings

Derived intersection rules are compatible with supersymmetry.

Rules apply to D-branes and solitonic 5-branes in string theories.

Open branes can have boundaries on other branes.

Abstract

We present a general rule determining how extremal branes can interesect in a configuration with zero binding energy. The rule is derived in a model independent way and in arbitrary spacetime dimensions $D$ by solving the equations of motion of gravity coupled to a dilaton and several different $n$-form field strengths. The intersection rules are all compatible with supersymmetry, although derived without using it. We then specialize to the branes occurring in type II string theories and in M-theory. We show that the intersection rules are consistent with the picture that open branes can have boundaries on some other branes. In particular, all the D-branes of dimension $q$, with $1\leq q \leq6$, can have boundaries on the solitonic 5-brane.