Phase diagrams of SU(N) gauge theories with fermions in various representations

We minimize the one-loop effective potential for SU(N) gauge theories including fermions with finite mass in the fundamental (F), adjoint (Adj), symmetric (S), and antisymmetric (AS) representations. We calculate the phase diagram on S ¹ × ℝ ³ as a function of the length of the compact dimension, β, and the fermion mass, m, for various N and N _f. We consider the effect of periodic boundary conditions [PBC(+)] on fermions as well as antiperiodic boundary conditions [ABC(-)]. With standard ABC(-) on fermions only the deconfined phase is found at one-loop for all representations considered. However, the use of PBC(+) produces a rich phase structure. These phases are distinguished by the eigenvalues of the Polyakov loop P. In the case of fundamental representation fermions [QCD(F,+)], a phase in which ReTr P is minimized (and negative) is favoured for all values of mβ. For N odd charge conjugation (C) symmetry is spontaneously broken in this phase due to O(1/N) effects. Minimization of the effective potential for QCD(AS/S,+) results in a phase where |ImTr P| is maximized, resulting in C-breaking for all N and all values of mβ, however, the partition function is the same up to O(1/N) corrections as when ABC are applied. Therefore, regarding orientifold planar equivalence, we argue that in the one-loop approximation C-breaking in QCD(AS/S,+) resulting from the application of PBC on fermions does not invalidate the large N equivalence with QCD(Adj,-). Similarly, with respect to orbifold planar equivalence, breaking of Z ₂ interchange symmetry resulting from application of PBC to bifundamental (BF) representation fermions does not invalidate equivalence with QCD(Adj,-) in the one-loop perturbative limit because the partition functions of QCD(BF,-) and QCD(BF,+) are the same. Of particular interest as well is the case of adjoint fermions where for 1$"N _f > 1 Majorana flavour confinement is obtained for sufficiently small mβ, and deconfinement for sufficiently large mβ. For N 3 these two phases are separated by one or more additional phases, some of which can be characterized as partially-confining phases.