18 - D-branes, gravity and gauge theory

Summary

As we learned in section 10.2, there are effectively two descriptions of the low energy dynamics of branes. One description uses the collective dynamics of the effetive world-volume field theory. In the case of N coincident D-branes, this is captured in string theory by the open string sectors which give a U(N) gauge theory with sixteen supercharges. The other description treats the brane as a soliton-like source of the various low energy closed string fields in the superstring theory. As such it has a description in terms of a classical solution of the low energy field equations. In both cases, we must remember that there is a whole tower of stringy dynamics which sits on top of this low energy physics, and we must understand in which situations this tower can be made irrelevant, or at least kept under control by a sensible expansion. To control string loops, we must work in a regime where g_s is small, so that we can trust the classical action that we wrote down for the supergravity. Similarly, working in the α′ → 0 limit ensures that we can safely ignore the possibility of the massive string states introducing corrections to our supergravity, and in the open string sector, that the truncation to gauge theory of the full Born–Infeld, etc., action, is sensible.