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This work presents the calculation of the relation between the bare couplingconstant g_0 and the MSbar-renormalized coupling g_MS, g_0 = Z_g(g_0,a\mu)g_MS, to 2 loops in perturbation theory, with fermions in an arbitraryrepresentation of the gauge group SU(N). Our calculation is performed usingoverlap fermions and Wilson gluons, and the background field technique has beenchosen for convenience. The corresponding results in the fundamentalrepresentation appear in our longer publication [arXiv:0709.4368].  The 3-loop coefficient of the bare beta-function, b_2^L, is extracted usingthe 2-loop expression for Z_g, and it is presented as a function of the overlapparameter rho, the number of fermion flavors (N_f) and the number of colors(N). We also provide the expression for the ratio Lambda_L/Lambda_MS, in anarbitrary representation. A plot of Lambda_L/Lambda_MS is given in the adjointrepresentation.

Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3-loop beta-function