Magnetic moments of branes and giant gravitons

We study the magnetic analogue of Myers' Dielectric Effect and, in some cas es, relate it to the blowing up of particles into branes, first investigate d by Greevy, Susskind and Toumbas. We show that D0-branes or gravitons in M -theory, moving in a magnetic four-form field strength background expand in to a non-commutative two sphere. Both examples of constant magnetic field a nd non-constant fields in curved backgrounds generated by branes are consid ered. We find, in all cases, another solution, consisting of a two-brane wr apping a classical two-sphere, which has all the quantum numbers of the D0- branes. Motivated by this, we investigate the blowing up of gravitons into branes in backgrounds different from AdS(m) X S-n. We find the phenomenon i s quite general. In many cases with less or even no supersymmetry we find a brane configuration which has the same quantum numbers and the same energy as a massless particle in supergravity.