Quantum link models with many rishon flavors and with many colors

Abstract

Quantum link models are a novel formulation of gauge theories in terms of discrete degrees of freedom. These degrees of freedom are described by quantum operators acting in a finite-dimensional Hilbert space. We show that for certain representations of the operator algebra, the usual Yang-Mills action is recovered in the continuum limit. The quantum operators can be expressed as bilinears of fermionic creation and annihilation operators called rishons. Using the rishon representation the quantum link Hamiltonian can be expressed entirely in terms of color-neutral operators. This allows us to study the large Nc limit of this model. In the 't Hooft limit we find an area law for the Wilson loop and a mass gap. Furthermore, the strong coupling expansion is a topological expansion in which graphs with handles and boundaries are suppressed.

D-theory: field quantization by dimensional reduction of discrete variables

“…On the analytic side, the discrete variables allow us to rewrite the theory in terms of fermionic rishon constituents of the bosonic fields. This may turn out to be useful when one studies the large N limit of various models [9]. In particular, one can now carry over powerful techniques developed for condensed matter systems (like the quantum Heisenberg model) to particle physics.…”

“…The two indices of a bosonic matrix field -for example, the two color indices of a gluon field matrix -can be separated because they are carried by two different rishons. This may lead to new ways to attack the large N limit of QCD and other interesting field theories [9]. D-theory is also attractive from a computational point of view.…”