Non-perturbative Brane effects

Question

In Johnson's Book about D-branes he gets the Tension of a D brane:

$$\tau_p = \frac{\sqrt{\pi}}{16 \kappa_0 g_s}(4\pi^2\alpha')^{(11-p)/2}$$

By performing a string amplitude calculation and comparing it with the QFT analogous (in the same fashion as in Polchinski lecture).

The tension of the brane is of order $g_s^{-1}$ and it seems that the conclusion is that the brane is a Non-perturbative object, what is the reason behind this? and which are the consecuences of a brane being non-perturbative?

Answer 1

The string theory perturbative expansion, similarly to QFT perturbative expansions, is weighted by powers of the string coupling $g_s$ and is reliable as long as the string coupling is small. In the small coupling regime the brane is non perturbative, indeed $1/g_s-> \infty$. This means that the tension of the brane (or the mass if you want) goes to infinity.

In this regime the brane is an heavy object, like an infinite mass wall of classical mechanics. For instance, in a scattering process of some closed string on a brane you can approximate the situation as if the brane exchange only momentum, whilst the energy is conserved (like a ball on a wall). Moreover as a first order approximation you can forget about the dynamics of the brane, since is so heavy.