Interacting branes, dual branes and dyonic branes:: a unifying lagrangian approach in D dimensions

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 in ow 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.