Quantum Chromodynamics with Eight and Twelve Degenerate Quark Flavors on the Lattice

This thesis is concerned with the behavior of non-abelian gauge theories with many flavors of fermions. In perturbation theory, an infrared fixed point is predicted to exist, and theories become conformal in the low energy limit, in non-abelian gauge theories with the number of fermions just below the threshold of losing asymptotic freedom. With the number of fermion flavors even smaller than the number required for conformal behavior, the coupling constant is expected to run slowly or "walk". However, the exact number of fermion flavors that is required for the conformal behavior is unknown. This thesis probes for non-perturbative evidence for such behavior by simulating SU(3) gauge theories on the lattice with eight and twelve degenerate fermions in the fundamental representation. The naive staggered fermion action with the DBW2 gauge action is used in the simulations. The exact RHMC algorithm with the Omelyan integrator is used for simulating all eight-flavor gauge configurations and twelve-flavor gauge configurations with large masses, mq ≥ 0.01. For the other twelve-flavor simulations with smaller masses, mq < 0.01, the exact HMC algorithm with multiple mass preconditioning and the force gradient integrator is used. Comparisons are also done with previous simulations, which used the Wilson plaquette gauge action and the inexact R algorithm. Both zero temperature (Nt = 32) and finite temperature physics are studied in this thesis. For system with eight flavors, the focus of the zero temperature simulations is on three values of input couplings β = 0.54, 0.56 and 0.58, with two or three quark masses for each coupling value. The zero-temperature, lattice artifact bulk transition found with the Wilson plaquette action in becomes a rapid cross-over with the DBW2 gauge action. At finite temperatures, a first order phase transition is observed at the strongest coupling, β = 0.54. For systems with twelve flavors, a large amount of simulation is done at values of input couplings from β = 0.45 to 0.50. A zero-temperature bulk transition is found with quark masses mq = 0.006 and 0.008, and it ends in a second order critical point at masses slightly larger than 0.008. The system shows a mass-dependent rapid cross-over with quark masses mq ≥ 0.01 around the lattice couplings from β = 0.46 to β = 0.48. A finite temperature study at β = 0.49 shows a drastic change of behavior in the screening masses and other observables, which suggests the existence of a finite temperature >transition. All the evidences gathered in this thesis support the argument that theories of both eight and twelve flavors of fermion in the fundamental representation of SU(3) gauge group are consistent with the behavior one would expected from a theory with spontaneously broken chiral symmetry. The strongest supporting evidence is the linearity of mÏ€2 ∝ mq at zero temperatures and the existence of a chiral symmetry restoring transition at finite temperatures. We note that other lattice simulations, also exploring the hadronic observables, arrive at a similar conclusion, while simulations of the running of the coupling have claimed that the 12 flavor theory is conformal.