Electric-Magnetic Duality and the Dirichlet Brane Spectrum

We clarify why the worldsheet evidence for a Dirichlet p-brane spectrum in the type II string theories with −2 ≤ p ≤ 9 is consistent with electric-magnetic duality in eleven target spacetime dimensions. We review our identification of the Dirichlet(-2)brane in hep-th/0007056 based upon the covariant worldsheet formalism for macroscopic loop amplitudes. We show that an operator formulation of the macroscopic loop amplitude must incorporate loop translation generators, ˆ P[C], into the standard boundary state formalism. We explain why our operator formulation is consistent with Schnakenburg and West’s observation that a contravariant one form generator in the global symmetry algebra of the massive type IIA supergravity has the correct commutation relations to be identified with the (-1)form supergravity potential predicted by electric-magnetic duality. 1