BPS GEODESICS IN N=2 SUPERSYMMETRIC YANG-MILLS THEORY

We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric ds(2) = \lambda sw\(2) Because the existence of such geodesics implie s the existence of BPS states in N = 2 supersymmetric Yang-Mills theor y, one can use these methods to study the BPS spectrum in various phas es of the Yang-Mills theory. By way of illustration, we show how, usin g our new methods, one can easily recover the known results for the N = 2 supersymmetric SU(2) pure gauge theory, and we show in detail how it also works for the N = 2, SU(2) theory coupled to a massive adjoint matter multiplet. (C) 1997 Published by Elsevier Science B.V.