Branes and holography

In this thesis I study aspects of the worldvolume dynamics of branes, under the limit in which they decouple from the bulk. The nongravitational theories that govern the dynamics of branes are particularly interesting because they are dual to gravitational theories in higher dimensions.;In a semi technical introduction to my thesis I review the arguments for this duality, and emphasize its importance for the string theorist. I also review checks of the duality conjecture, and some of the work it has inspired.;The worldvolume theory of M2, M5 and D3 branes is superconformally invariant. In the second chapter of this thesis, I investigate the restrictions imposed by superconformal invariance on any quantum field theory, thereby obtaining restrictions on the operator spectrum in the worldvolume theories of these branes. In the third chapter I compute the spectrum of chiral primary operators in the theory of M2 and M5 branes using the Maldacena duality. In the fourth chapter I go on to compute the three point functions of all chiral operators on the worldvolume of the D3 brane, once again employing its dual gravitational description. In chapter five I study the decoupled theory of the IIA NS5-brane, using its spacetime description, and compute the two point function of its stress energy tensor. In chapter 6 I study the perturbative dynamics of noncommutative field theories; the class of theories that describe decoupled D-branes in the presence of a constant NS-NS 2 form B field.