RENORMALIZATION FLOW AND GEODESICS ON THE MODULI SPACE OF 4-DIMENSIONAL N=2 SUPERSYMMETRIC YANG-MILLS THEORY

It is shown that the beta-functions for four dimensional N = 2 supersy mmetric Yang-Mills theory without matter give integral curves on the m oduli space some of which are geodesics of the natural metric on the m oduli space. In particular the flow lines which cross-over from the we ak coupling limit (asymptotically free theory) to the singular points, representing the strong coupling limit, are geodesics. A possible con nection with irreversibility is discussed. (C) 1998 Elsevier Science B .V.