Why cannot a fundamental string couple to the R-R gauge field $C_{\mu\nu}$?

Question

People usually say that D-branes can carry R-R charges, or can couple to R-R sector gauge fields. But why a fundamental string cannot couple to a 2-form R-R sector gauge field? What's the essential different between a D-string (D1-brane) and a fundamental string?

Answer 1

Quote from "Lectures on D-branes, Constantin P. Bachas"

Now within type-II perturbation theory there are no such elementary RR sources. Indeed, if a closed-string state were a source for a RR (p + 1)-form,then the trilinear coupling

$$< closed| C_{(p+1)} |closed >$$

would not vanish. This is impossible because the coupling involves an odd number of left-moving (and of right-moving) fermion emission vertices, so that the corresponding correlator vanishes automatically on any closed Riemann surface. What this arguments shows, in particular, is that fundamental closed strings do not couple ‘electrically’ to the Ramond-Ramond two-form. It is significant, as we will see, that in the presence of worldsheet boundaries this simple argument will fail.

Answer 2

Just because the D1-string has the right dimensionality to couple to a 2-form RR potential doesn't mean that it must. The same line of reasoning could be applied to the more familiar case of electromagnetism; you could easily imagine a world with 2 different U(1) gauge fields. There could be particles that are charged under gauge field #1, particles charged under gauge field #2, and even particles charged under both. The essential point here is that just because you are given a 0-dimensional brane (particle), you haven't learned anything about what fields it is charged under. The same is true in string theory. In order to determine what brane couples to which field, you would need more information than just the dimensionality.