  Nontrivial Bianchi identities with local magnetic sources are solved by
recognizing that gauge potentials are sections rather than globally defined
functions, but properly accounting for the source degrees of freedom requires a
modification of the field strength. Following work by Teitelboim and by
Cariglia and Lechner, we extend Dirac's string formalism for monopoles to
D-branes in type IIA and IIB string theory. We give novel derivations of
brane-induced Chern-Simons terms in the supergravity actions, including a
prescription for integrating over potentials in the presence of magnetic
sources. We give a noncovariant formulation of the IIB theory, keeping only the
independent degrees of freedom of the self-dual 4-form potential. Finally, it
is well-known that D8-branes source the mass parameter of IIA supergravity; we
show that the additional couplings of the massive IIA supergravity, including
on other D-brane worldvolumes, are a consequence of the corresponding Dirac
branes.
