  This paper presents a general covariant lagrangian framework for the dynamics
of a system of closed n-branes and dual (D-n-4)-branes in D dimensions,
interacting with a dynamical (n+1)-form gauge potential. The framework proves
sufficiently general to include also a coupling of the branes to (the bosonic
sector of) a dynamical supergravity theory. We provide a manifestly
Lorentz-invariant and S-duality symmetric Lagrangian, involving the (n+1)-form
gauge potential and its dual (D-n-3)-form gauge potential in a symmetric way.
The corresponding action depends on generalized Dirac-strings. The requirement
of string-independence of the action leads to Dirac-Schwinger quantization
conditions for the charges of branes and dual branes, but produces also
additional constraints on the possible interactions. It turns out that a system
of interacting dyonic branes admits two quantum mechanically inequivalent
formulations, involving inequivalent quantization conditions. Asymmetric
formulations involving only a single vector potential are also given. For the
special cases of dyonic branes in even dimensions known results are easily
recovered. As a relevant application of the method we write an effective action
which implements the inflow anomaly cancellation mechanism for interacting
heterotic strings and five-branes in D=10. A consistent realization of this
mechanism requires, in fact, dynamical p-form potentials and a systematic
introduction of Dirac-strings.

High Energy Physics - Theory