Born-Infeld actions and D-brane physics

Some very interesting things can be learned about the physics of D-branes by studying the solutions of the effective action for low-energy fluctuations of the D-brane about its ground state. Many pieces of evidence indicate that the correct action is essentially the Born-Infeld action for nonlinear electrodynamics (with some modifications to adapt it to the D-brane context). We motivate this description of the dynamics of branes and then explore a series of applications, starting with the simple case of branes in hat space and working our way up to branes in the curved backgrounds of large numbers of other branes. Some of these applications make contact with the AdS/CFT conjecture of Maldacena in interesting ways and these are developed in some detail.