Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets
arXiv:hep-th/9904087 · doi:10.1016/S0550-3213(99)00498-8
Abstract
We compute instanton corrections to the low energy effective prepotential of N=2 supersymmetric theories in a variety of cases, including all classical gauge groups and even number of fundamental matter hypermultiplets. To this end, we take profit of a set of first- and second-order equations for the logarithmic derivatives of the prepotential with respect to the dynamical scale expressed in terms of Riemann's theta-function. These equations emerge in the context of the Whitham hierarchy approach to the low-energy Seiberg--Witten solution of supersymmetric gauge theories. Our procedure is recursive and allows to compute the effective prepotential to arbitrary order in a remarkably straightforward way. General expressions for up to three-instanton corrections are given. We illustrate the method with explicit expressions for several cases.
25 pages, LaTeX2e, no figures; v2: Concluding remarks expanded, other minor changes. Final version to be published in Nuclear Physics B
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