The Coulomb branch of gauge theory from rotating branes

At zero temperature the Coulomb Branch of N = 4 super Yang-Mills theory is described in supergravity by multi-center solutions with D3-brane charge. A t finite temperature and chemical potential the vacuum degeneracy is lifted , and minima of the free energy are shown to have a supergravity descriptio n 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 rot ating black D3-branes. The low energy excitations of the system appear to b e governed by an effective string theory which is related to the singularit y in spacetime.