Supersymmetric Yang-Mills Systems And Integrable Systems

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Abstract

The Coulomb branch of \(N=2\) supersymmetric gauge theories in four dimensions is described in general by an integrable Hamiltonian system in the holomorphic sense. A natural construction of such systems comes from two-dimensional gauge theory and spectral curves. Starting from this point of view, we propose an integrable system relevant to the \(N=2\) \(SU(n)\) gauge theory with a hypermultiplet in the adjoint representation, and offer much evidence that it is correct. The model has an \(SL(2,{\bf Z})\) \(S\)-duality group (with the central element \(-1\) of \(SL(2,{\bf Z})\) acting as charge conjugation); \(SL(2,{\bf Z})\) permutes the Higgs, confining, and oblique confining phases in the expected fashion. We also study more exotic phases.

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Is Open Access

The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

Alon E. Faraggi, Philip Argyres (1994)

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.