Higher representations: Confinement and large N

We investigate the confining phase transition as a function of temperature for theories with dynamical fermions in the two index symmetric and antisymmetric representation of the gauge group. By studying the properties of the center of the gauge group we predict for an even number of colors a confining phase transition, if second order, to be in the universality class of Ising in three dimensions. This is due to the fact that the center group symmetry does not break completely for an even number of colors. For an odd number of colors the center group symmetry breaks completely. This pattern remains unaltered at a large number of colors. The confining/deconfining phase transition in these theories at large and finite N is not mapped in the one of super Yang-Mills theory. We extend the Polyakov loop effective theory to describe the confining phase transition of the theories studied here for a generic number of colors. Our results are not modified when adding matter in the same higher dimensional representations of the gauge group. We comment on the interplay between confinement and chiral symmetry in these theories and suggest that they are ideal laboratories to shed light on this issue also for ordinary QCD. We compare the free energy as a function of temperature for different theories. We find that the conjectured thermal inequality between the infrared and ultraviolet degrees of freedom computed using the free energy does not lead to new constraints on asymptotically free theories with fermions in higher dimensional representations of the gauge group. Since the center of the gauge group is an important quantity for the confinement properties at zero temperature our results are relevant here as well. © 2005 The American Physical Society