Large-N reduction in QCD-like theories with massive adjoint fermions

Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four-and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, the center-symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large volume limit through the Eguchi-Kawai equivalence. A finite-temperature version of volume independence implies that thermodynamics on R-3 x S-1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this nonperturbatively, we numerically study both zero-and one-dimensional theories by using Monte Carlo simulation. The order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1(3) x 2 lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a nonperturbative formulation of the noncommutative Yang-Mills theory.