  Recently a non-perturbative formula for the RG flow between UV and IR fixed
points of the coefficient in the trace of the energy momentum tensor of the
Euler density has been obtained for N=1 SUSY gauge theories by relating the
trace and R-current anomalies. This result is compared here with an earlier
perturbation theory analysis based on a naturally defined metric on the space
of couplings for general renormalisable quantum field theories. This approach
is specialised to N=1 supersymmetric theories and extended, using consistency
arguments, to obtain the Euler coefficient at fixed points to 4-loops. The
result agrees completely, to this order, with the exact formula.
