| In this dissertation, we describe our studies on phases of gauge theories in the infrared. In Part I, we study the phases of chiral gauge theories whose spontaneous symmetry breaking is due to the strong attractive interaction between fermions. We discuss two chiral SU(N) gauge theories involving fermions in the symmetric and antisymmetric two-index tensor representations respectively. In addition to global anomaly matching, we employ a recently proposed inequality constraint on the number of effective low energy degrees of freedom of a theory, based on the thermodynamic free energy. Several possible zero temperature phases are consistent with the constraints. A simple picture for the phase structure emerges if these theories choose the phase, consistent with global anomaly matching, that minimizes the massless degree of freedom count defined through the free energy. In Part II, we study QCD at high density. In this region, due to the well-known BCS mechanism, even a small attractive interaction around the Fermi surface can induce a diquark condensate which breaks the color gauge symmetry. Thus a color superconducting phase appears. We construct an effective Lagrangian for the two-flavor case by using the nonlinear realization The light degrees of freedom, as required by global anomaly matching conditions, contain massless fermions. We also extend the effective Lagrangians for three flavors and two flavors to include the electroweak interaction. For the three-flavor case, we show that the decay process π0 into two physical photons is identical to the zero density case once we use the new π decay constant and the modified electric charge. For the two-flavor case, we find that the coupling of quarks to the neutral vector boson Z0 could be modified with respect to the zero density case. |
