TL;DR
This paper explores extracting Seiberg-Witten curves from Nekrasov's prepotential series, proposing a method for non-hyperelliptic models and validating results with instanton counting.
Contribution
It introduces a novel approach to derive Seiberg-Witten curves for complex gauge theories, including non-hyperelliptic cases, and verifies instanton corrections against direct computations.
Findings
Successfully derived Seiberg-Witten curves for specific models.
Validated instanton corrections up to two instantons.
Extended methods to non-hyperelliptic curves.
Abstract
We investigate the possibility to extract Seiberg-Witten curves from the formal series for the prepotential, which was obtained by the Nekrasov approach. A method for models whose Seiberg-Witten curves are not hyperelliptic is proposed. It is applied to the SU(N) model with one symmetric or antisymmetric representations as well as for SU(N_1)xSU(N_2) model with (N_1,N_2) or (N_1,\bar{N}_2) bifundamental matter. Solutions are compared with known results. For the gauge group product we have checked the instanton corrections which follow from our curves against direct instanton counting computations up to two instantons.
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