Finite volume phases of large-N gauge theories with massive adjoint fermions

doi:10.1088/1126-6708/2009/11/008

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Timothy J. Hollowood and Joyce C. Myers JHEP11(2009)008 doi:10.1088/1126-6708/2009/11/008

Finite volume phases of large-N gauge theories with massive adjoint fermions

Timothy J. Hollowood and Joyce C. Myers

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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 Bbb Z

_p subgroup of the centre symmetry. In these Bbb 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 S³) only the confined phase exists. The large N phase diagram is consistent with the finite N result and with other approaches based on Bbb R

³ × S¹ calculations and lattice simulations.

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Finite volume phases of large-N gauge theories with massive adjoint fermions

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