Phases of circle-compactified QCD with adjoint fermions at finite density

We study chemical-potential dependence of confinement and mass gap in QCD with adjoint fermions in spacetime with one spatial compact direction. By calculating the one-loop effective potential for the Wilson line in the presence of a chemical potential, we show that a center-symmetric phase and a center-broken phase alternate when the chemical potential in units of the compactification scale is increased. In the center-symmetric phase we use semiclassical methods to show that photons in the magnetic bion plasma acquire a mass gap that grows with the chemical potential as a result of anisotropic interactions between monopole-instantons. For the neutral fermionic sector which remains gapless perturbatively, there are two possibilities at a nonperturbative level: either to remain gapless (unbroken global symmetry) or to undergo a novel superfluid transition through a four-fermion interaction (broken global symmetry). If the latter is the case, this leads to an energy gap of quarks proportional to a new nonperturbative scale L-1exp[-1/(g4μL)], where L denotes the circumference of S1, the low-energy physics is described by a Nambu-Goldstone mode associated with the baryon number, and there exists a new type of BEC-BCS crossover of the diquark pairing as a function of the compactification scale at a small chemical potential.