The running of the coupling in SU(N) pure gauge theories

The running of the coupling is studied in SU(4) gauge theory using the Schrodinger functional technique. Up to energies of the order of the square root of the string tension C, the running is found to agree with the two-loop perturbative formula. Relating the perturbative to the non-perturbative regime of the running and converting to the (MS) over bar scheme allows one to extract the ratio Lambda(MS) over bar/root sigma . The result is then used in combination with similar calculations present in the literature for SU(2) and SU(3) to extract Lambda(MS) over bar/root sigma in the large N limit. Our results for N = 3, 4 agree with a recent study of the same quantity performed using the Parisi mean field scheme as an intermediate scheme, while Lambda(MS) over bar/root sigma in SU(2) turns out to differ by 2.5%. Possible explanations of this discrepancy are discussed. (c) 2008 Elsevier B.V. All rights reserved.