Simple Singularities and N=2 Supersymmetric Yang-Mills Theory

Abstract

We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to underly the quantum moduli space of $SU(n)$ N=2 supersymmetric gauge theory. These curves have an obvious generalization to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities. To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced. We also give some remarks on a possible relation to string theory.

13p, harvmac/lanlmac with hyperlinks 1 uuencoded PostScript figure appended (Some inconsistencies and typos were corrected, we also dropped our conjectures for the monodromies at strong coupling, of which we know now that they are different.)

References in corpus (2)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• On the Geometry of Moduli Space of Vacua in N=2 Supersymmetric Yang-Mills Theory

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