Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-07-21
JHEP 0911:008,2009
Physics
High Energy Physics
High Energy Physics - Theory
31 pages, 12 figures, jhep3 format; v2: references and small clarifications added, justification added for finite N calculatio
Scientific paper
10.1088/1126-6708/2009/11/008
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 S^3 x S^1. 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 S^1. 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 Z_p subgroup of the centre symmetry. In these Z_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 S^3) only the confined phase exists. The large N phase diagram is consistent with the finite N result and with other approaches based on R^3 x S^1 calculations and lattice simulations.
Hollowood Timothy J.
Myers Joyce C.
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