Finite volume phases of large-Ngauge theories with massive adjoint fermions

Abstract

The phase structure of QCD-like gauge theories with fermions in various representations is an interesting but generally analytically intractable problem. One way to ensure weak coupling is to define the theory in a small finite volume, in this case S3 × S1. Genuine phase transitions can then occur in the large N theory. Here, we use this technique to investigate SU(N) gauge theory with a number Nf of massive adjoint-valued Majorana fermions having non-thermal boundary conditions around S1. For Nf = 1 we find a line of transitions that separate the weak-coupling analogues of the confined and de-confined phases for which the density of eigenvalues of the Wilson line transform from the uniform distribution to a gapped distribution. However, the situation for Nf > 1 is much richer and a series of weak-coupling analogues of partially-confined phases appear which leave unbroken a psubgroup of the centre symmetry. In these p phases the eigenvalue density has p gaps and they are separated from the confining phase and from one-another by first order phase transitions. We show that for small enough mR (the mass of the fermions times the radius of the S3) only the confined phase exists. The large N phase diagram is consistent with the finite N result and with other approaches based on 3 × S1 calculations and lattice simulations.