Finite Volume Phases of Large N Gauge 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 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.

31 pages, 12 figures, jhep3 format; v2: references and small clarifications added, justification added for finite N calculations

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Cited by in corpus (10)

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• The infrared dynamics of Minimal Walking Technicolor
• Large-N reduction in QCD-like theories with massive adjoint fermions
• Large-N reduction of SU(N) Yang-Mills theory with massive adjoint overlap fermions
• Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition
• Recent results in large-N lattice gauge theories
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• Confinement on $R^3\times S^1$: continuum and lattice
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories
• Large-N reduction with adjoint Wilson fermions