Confinement/deconfinement transition of large N gauge theories with [formula omitted] fundamentals: [formula omitted] finite

Abstract

We consider large N zero-coupling d-dimensional U ( N ) gauge theories, with N f matter fields in the fundamental representation on a compact spatial manifold S d − 1 × time, with N f / N finite. The Gauss' law constraint induces interactions among the fields, in spite of the zero-coupling. This class of theories undergo a 3rd order deconfinement phase transition at a temperature T c proportional to the inverse length scale of the compact manifold. The low-temperature phase has a free-energy of O ( N f 2 ) , interpreted as that of a gas of (color singlet) mesons and glueballs. The high-temperature (deconfinement) phase has a free energy of order N 2 f ( N f / N , T ) , which is interpreted as that of a gas of gluons and of fundamental and anti-fundamental matter states. This suggests the existence of a dual string theory, and a transition to a black hole at high temperature.