Adjoint Quarks Research Articles

Charge screening, large- N, and the abelian projection model of confinement

We point out that the abelian projection theory of quark confinement is in conflict with certain large- N predictions. According to both large- N and lattice strong-coupling arguments, the perimeter law behavior of adjoint Wilson loops at large scales is due to charge screening, and is suppressed relative to the area term by a factor of 1/ N 2. In the abelian projection theory, however, the perimeter law is due to the fact that N − 1 out of N 2 − 1 adjoint quark degrees of freedom are (abelian) neutral and unconfined; the suppression factor relative to the area law is thus only 1/ N. We study numerically the behavior of Wilson loops and Polyakov lines with insertions of (abelian) charge projection operators, in maximal abelian gauge. It appears from our data that the forces between abelian charged, and abelian neutral adjoint quarks are not significantly different. We also show via the lattice strong-coupling expansion that, at least at strong couplings, QCD flux tubes attract one another, whereas vortices in type-II superconductors repel.

From baglike models to the large-Nc limit via the Abelian projection.

't Hooft proposed a model where quarks are confined by a chromomagnetic Meissner effect along the N-1 U(1) directions of the maximal Abelian subgroup of SU(N). This is the Abelian projection. I show that this model successfully interpolates from low N, where quarks are confined in a baglike region of perturbative vacuum embedded in the true nonperturbative vacuum, to the large-N limit. At large N quarks are confined in a ''shallow'' nonperturbative medium and the string tension is an N-independent constant. Confinement of adjoint quarks also properly evolves from screening at small N to confinement at infinite N with a string tension twice as large as for quarks in the fundamental representation.

Hierarchal Mass Scales in Lattice Gauge Theories with Dynamical, Light Fermions

SU(2) lattice gauge theory with two Dirac species of light, adjoint fermions included in the dynamics is simulated at finite temperatures by use of the microcanonical algorithm. The theory contains two natural mass scales, the string tension for heavy, fundamental quarks and the chiral-symmetry-breaking scale of light, adjoint quarks. The two scales are found to be distinct. This result generalizes earlier results obtained in the quenched approximation and should encourage builders of hierarchal models.

Studies of chiral symmetry breaking in SU(2) lattice gauge theory

We study chiral symmetry breaking ( χSB) in SU(2) lattice gauge theory with quarks in the l = 1 2 , l = 1, l = 3 2 , and l = 2 representations of the color group. We perform Monte Carlo evaluations of 〈 ψψ〉 in the quenched approximation and extract the relevant length scales for χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain T l = 1/T l = 1 2 ∼ 8 . Our results for the higher representations, l = 3 2 and l = 2 , are consistent with Casimir scaling and give C 2 g mom 2 ∼ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.