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

This paper presents a general covariant lagrangian framework for the dynamicsof 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 provessufficiently general to include also a coupling of the branes to (the bosonicsector of) a dynamical supergravity theory. We provide a manifestlyLorentz-invariant and S-duality symmetric Lagrangian, involving the (n+1)-formgauge potential and its dual (D-n-3)-form gauge potential in a symmetric way.The corresponding action depends on generalized Dirac-strings. The requirementof string-independence of the action leads to Dirac-Schwinger quantizationconditions for the charges of branes and dual branes, but produces alsoadditional constraints on the possible interactions. It turns out that a systemof interacting dyonic branes admits two quantum mechanically inequivalentformulations, involving inequivalent quantization conditions. Asymmetricformulations involving only a single vector potential are also given. For thespecial cases of dyonic branes in even dimensions known results are easilyrecovered. As a relevant application of the method we write an effective actionwhich implements the inflow anomaly cancellation mechanism for interactingheterotic strings and five-branes in D=10. A consistent realization of thismechanism requires, in fact, dynamical p-form potentials and a systematicintroduction of Dirac-strings.Comment: 36 pages, LaTeX, no figure