Dynamical stabilization of runaway potentials at finite density

We study four-dimensional non-Abelian gauge theories with classical moduli. Introducing a chemical potential for a flavor charge causes moduli to become unstable and start condensing. We show that the moduli condensation in the presence of a chemical potential generates non-Abelian field strength condensates. These condensates are homogeneous but non-isotropic. The end point of the condensation process is a stable homogeneous, but non-isotropic, vacuum in which both gauge and flavor symmetries and the rotational invariance are spontaneously broken. Possible applications of this phenomenon for the gauge theory/string theory correspondence and in cosmology are briefly discussed.