In the exploration of viable models of dynamical electroweak symmetry breaking, it is essential to locate the lower end of the conformal window and know the mass anomalous dimensions there for a variety of gauge theories. We calculate, with the Schro
dinger functional scheme, the running coupling constant and the mass anomalous dimension of SU(2) gauge theory with six massless Dirac fermions in the fundamental representation. The calculations are performed on $6^4$ - $24^4$ lattices over a wide range of lattice bare couplings to take the continuum limit. The discretization errors for both quantities are removed perturbatively. We find that the running slows down and comes to a stop at $0.06 lesssim 1/g^2 lesssim 0.15$ where the mass anomalous dimension is estimated to be $0.26 lesssim gamma^*_m lesssim 0.74$.
We investigate the chiral properties of SU(2) gauge theory with six flavors, i.e. six light Dirac fermions in the fundamental representations by lattice simulation, and point out that the spontaneous breakdown of chiral symmetry does not occur in thi
s system. The quark mass dependence of the mesonic spectrum provides an evidence for such a possibility. The decay constant tends to be increased by the finite size effect, which is opposite to the behavior predicted by chiral perturbation theory and indicates that the long distance dynamics in the six-flavor theory could be different from the theory with chiral symmetry breaking. The subtracted chiral condensate, whose utility is demonstrated by the simulation of two-flavor theory, is shown to vanish in the chiral limit within the precision of available data.
