Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold

Details Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold

1997-03-31

arxiv.org/abs/hep-th/9703228v2

Nucl.Phys. B502 (1997) 59-93

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, LaTeX. Typos corrected

Scientific paper

10.1016/S0550-3213(97)00454-9

We investigate quantum effects on the Coulomb branch of three-dimensional N=4 supersymmetric gauge theory with gauge group SU(2). We calculate perturbative and one-instanton contributions to the Wilsonian effective action using standard weak-coupling methods. Unlike the four-dimensional case, and despite supersymmetry, the contribution of non-zero modes to the instanton measure does not cancel. Our results allow us to fix the weak-coupling boundary conditions for the differential equations which determine the hyper-Kahler metric on the quantum moduli space. We confirm the proposal of Seiberg and Witten that the Coulomb branch is equivalent, as a hyper-Kahler manifold, to the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin.

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