The Super D9-Brane and its Truncations

TL;DR

The paper analyzes two inequivalent truncations of the super D9-brane in IIB supergravity—the Heterotic and Type I truncations—and shows that both yield $N=1$ nonlinear supersymmetry on the brane with a $D=10$ cosmological constant. The Heterotic truncation leads to an Abelian $D=10$ vector multiplet, while the Type I truncation produces a ten-dimensional Volkov–Akulov action for a Majorana–Weyl fermion, with a novel reformulation via the RR 10-form $C^{(10)}$. The analysis relies on extending IIB $Z_2$ symmetries to the full super D9-brane action and on the introduction of two 10-forms to write a gauge-invariant Wess–Zumino term. The results generalize to all spacetime-filling D-branes ($D=3,4,6,10$) and suggest avenues for non-Abelian generalizations and connections to Type I string theory with orientifold planes.

Abstract

We consider two inequivalent truncations of the super D9--brane: the ``Heterotic'' and the ``Type I'' truncation. Both of them lead to an N=1 nonlinear supersymmetrization of the D=10 cosmological constant. The propagating degrees of freedom in the Heterotic and Type I truncation are given by the components of a D=10 vector multiplet and a single Majorana-Weyl spinor, respectively. As a by-product we find that, after the Type I truncation, the Ramond-Ramond super ten-form provides an interesting reformulation of the Volkov-Akulov action. These results can be extended to all dimensions in which spacetime filling D-branes exist, i.e. D=3,4,6 and 10.