Abstract
At zero temperature the Coulomb Branch of 
= 4 super Yang-Mills theory
is described in supergravity by multi-center solutions with
D3-brane charge. At finite temperature and chemical potential
the vacuum degeneracy
is lifted, and minima of the free energy are shown to have a
supergravity description as rotating black D3-branes.
In the extreme limit these solutions single out
preferred points on the moduli space that can be interpreted as
simple distributions of branes - for instance, a uniformly charged
planar disc. We exploit this geometrical representation to study the
thermodynamics of rotating black D3-branes.
The low energy excitations of the system appear to be governed
by an effective string theory which is related to the singularity
in spacetime.