Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory

Details Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory

2000-06-07

arxiv.org/abs/hep-th/0006050v2

Commun.Math.Phys. 218 (2001) 333-371

Physics

High Energy Physics

High Energy Physics - Theory

48 pages, AMS latex. v2: several minor errors corrected, exposition improved

Scientific paper

10.1007/PL00005558

We study Bogomolny equations on $R^2\times S^1$. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk\"ahler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of $k$ periodic monopoles provides the exact solution of ${\cal N}=2$ super Yang-Mills theory with gauge group $SU(k)$ compactified on a circle of arbitrary radius.

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