Large-Nreduction 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 R³×S¹ 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 1³×2 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.