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 Schrodinger 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 $0.26 lesssim gamma^*_m lesssim 0.74$.
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