Our experience with many physical systems tells us that usually when a symmetry is spontaneously broken at low temperatures, it is restored upon increasing the temperature sufficiently.  The abundance of such systems raises the question of whether this is a universal feature of all quantum systems. In this talk, I will present examples of (3+1)-dimensional non-supersymmetric large N gauge theories which demonstrate violations of the above feature. I will argue that in the N tending to infinity limit, these theories have conformal manifolds which survive under all loop corrections to the beta functions of the couplings. I will show that under certain conditions, a subset of points on such a conformal manifold demonstrates the spontaneous breaking of a global symmetry at all nonzero temperatures. Furthermore, I will demonstrate that this symmetry breaking is accompanied by the Higgsing of a subset of gauge bosons leading the system to be in a persistent Brout-Englert-Higgs phase.

 

We study operators with a bare dimension that grows as N^2 in the large N limit. These operators are labeled by a Young diagram with p long rows, as well as a graph, with p nodes. The dilatation operator describing the mixing of these operators defines a Hamiltonian for excitations hopping on this graph. The scrambling and equilibration of the resulting dynamics is studied.