  The Schrodinger functional is used to define a renormalised coupling for pure
SU(4) Yang-Mills theory, with Wilson action and suitably selected boundary
conditions on the link field. The coupling, which runs with the size of the
lattice, is then determined by a finite-size scaling technique through a large
range of momenta, thereby allowing a connection to be made between the high
energy regime and the low energy non-perturbative regime, where contact is made
with the physical scale of the theory. Using data from previous SU(2) and SU(3)
simulations obtained with the same technique, the running of the 't Hooft
coupling defined through the Schrodinger functional is studied, and we check
whether the large-N expectation that g^2*N is a universal function of the
energy scale E holds down to energies of the order of the string tension.
Finally, we determine Lambda_SF in units of the string tension as a function of
N at leading order in 1/N^2.
