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      Integrable systems and supersymmetric gauge theory

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          Abstract

          After the work of Seiberg and Witten, it has been seen that the dynamics of N=2 Yang-Mills theory is governed by a Riemann surface \(\Sigma\). In particular, the integral of a special differential \(\lambda_{SW}\) over (a subset of) the periods of \(\Sigma\) gives the mass formula for BPS-saturated states. We show that, for each simple group \(G\), the Riemann surface is a spectral curve of the periodic Toda lattice for the dual group, \(G^\vee\), whose affine Dynkin diagram is the dual of that of \(G\). This curve is not unique, rather it depends on the choice of a representation \(\rho\) of \(G^\vee\); however, different choices of \(\rho\) lead to equivalent constructions. The Seiberg-Witten differential \(\lambda_{SW}\) is naturally expressed in Toda variables, and the N=2 Yang-Mills pre-potential is the free energy of a topological field theory defined by the data \(\Sigma_{\gg,\rho}\) and \(\lambda_{SW}\).

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

          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.
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            The τ-function of the universal whitham hierarchy, matrix models and topological field theories

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              The Coulomb Phase of N=2 Supersymmetric QCD

              We present an explicit non-perturbative solution of N=2 supersymmetric SU(N_c) gauge theory with N_f \le 2N_c flavors generalizing results of Seiberg and Witten for N_c=2.
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                Author and article information

                Journal
                27 September 1995
                1995-10-06
                Article
                10.1016/0550-3213(95)00588-9
                hep-th/9509161
                098a0ebb-0a67-409a-8db1-dc73c3eed0c1
                History
                Custom metadata
                EFI-95-61, USC-95/025
                Nucl.Phys.B459:97-112,1996
                20 pages, latex, 3 uuencoded figures (needs epsf.tex); minor errors corrected, references added
                hep-th

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