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 N_f of massive adjoint-valued Majorana fermions having non-thermal boundary conditions around S¹. For N_f = 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 N_f > 1 is much richer and a series of weak-coupling analogues of partially-confined phases appear which leave unbroken a _p subgroup 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.

Key words: 1/N Expansion; Spontaneous Symmetry Breaking; Confinement

E-print number: 0907.3665
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Received 22 September 2009, accepted for publication 13 October 2009
Published 4 November 2009