# Finite Volume Phases of Large N Gauge Theories with Massive Adjoint Fermions - High Energy Physics - Theory

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Abstract: The phase structure of QCD-like gauge theories with fermions in variousrepresentations is an interesting but generally analytically intractableproblem. One way to ensure weak coupling is to define the theory in a smallfinite volume, in this case S^3 x S^1. Genuine phase transitions can then occurin the large N theory. Here, we use this technique to investigate SUN gaugetheory with a number N f of massive adjoint-valued Majorana fermions havingnon-thermal boundary conditions around S^1. For N f =1 we find a line oftransitions that separate the weak-coupling analogues of the confined andde-confined phases for which the density of eigenvalues of the Wilson linetransform from the uniform distribution to a gapped distribution. However, thesituation for N f >1 is much richer and a series of weak-coupling analogues ofpartially-confined phases appear which leave unbroken a Z p subgroup of thecentre symmetry. In these Z p phases the eigenvalue density has p gaps and theyare separated from the confining phase and from one-another by first orderphase transitions. We show that for small enough mR the mass of the fermionstimes the radius of the S^3 only the confined phase exists. The large N phasediagram is consistent with the finite N result and with other approaches basedon R^3 x S^1 calculations and lattice simulations.

Author: ** Timothy J. Hollowood, Joyce C. Myers**

Source: https://arxiv.org/