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In the famous paper by Polchinski where he shows that D-branes are sourcing RR fields, he says (before we known the result) that RR sources must be objects with tension going like $1/g_s$ (page two of the paper). How do we know that? I understand that it must be non-perturbative in $g_s$ (essentially because strings aren't charged under RR fields), but why it has to be precisely $1/g_s$ ?

Thanks.

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He doesn't really "state" the result without deriving it. He derives it. See e.g. this sentence on page 2:

It is further shown that since the D-brane tension arises from the disk, it scales in string units as $g^{−1}$, $g$ being the closed string coupling

The tension of D-branes goes like $1/g_s$ because the tension may be calculated from the disk diagram (stringy world sheet of the disk topology) and the disk has the Euler characteristic $\chi=1$ (like a point) so the corresponding term to the partition sum scales like $1/g_s$. The leading terms in the bosonic string action go like $1/g_s^2$ because they result from the spherical world sheet and the sphere has $\chi=2$. It is no coincidence that the D-brane tension has a halved value of $\chi$ so the tension is a geometric mean of $1$ and $1/g_s^2$; after all, the disk is topologically the same thing as a hemisphere.

Polchinski has known that the tension should come from the disk pretty much from the late 1980s when he and others realized that D-branes are linked to Dirichlet/mixed boundary conditions on the world sheet boundaries and the disk is the simplest world sheet topology with a boundary.

The RR-charges of these objects are determined by the BPS condition (force is zero because they're mutually supersymmetric), so in some normalization/convention for the charges, we have "tension equals charge density" so the charge density is also $1/g_s$.

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