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It is indeed compactly-supported Poincare duality via currents, for which the standard reference is de Rham's Differentiable Manifolds. For example, the Dirac delta function is the dual of a point! Anyway, to get to a quick understanding, see the beginning of Section 7.3 of Nicolaescu's notes http://www3.nd.edu/~lnicolae/Lectures.pdf

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These branes are being smashed together so that once they are closer than the string length they become indistinguishable from a single brane. These branes have $U(N_c)$ gauge group, and in this space there is a vector. In a generic sense all Lie algebras are like the harmonic oscillator with $a$, $a^\dagger$ and $a^\dagger a$ in the structure of roots and ...

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It's a bit strange because the OP basically repeats the same statement twice. First, he says that he understands it and second, he says that he doesn't. But let's try to avoid these detailed surprising aspects of the question and try to explain what's going on, anyway or again. Type I/II strings have spacetime supercharges $Q_a$ that are constructed purely ...

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Your conclusion is true only for $N=1$ supersymmetry. If I have extended supersymmetry, then I can start from the graviton state and end up in a scalar state. What you are saying is true. If I have D-branes, I need to consider projections of all fields into normal and tangent directions onto the D-brane. The world-volume theory of the D-brane will contain ...

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For the coupling of p-brane Gauge fields to B 2-forms and U(1) Gauge fields check the Chern-Simons effective action for Dp branes. For coupling to fermions check some SUGRA actions, for instance the D=11 SUGRA has the graviton, the gravitino and 3-form Gauge field. Coupling to scalars is omnipresent in dimensional reductions of SUGRA actions.

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