BPS geodesics in N = 2 supersymmetric Yang-Mills theory Original Research Article

We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric ds2 = |λsw|2. Because the existence of such geodesics implies the existence of BPS states in N = 2 supersymmetric Yang-Mills theory, one can use these methods to study the BPS spectrum in various phases of the Yang-Mills theory. By way of illustration, we show how, using 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.