Multi-instantons in R^4 and Minimal Surfaces in R^{2,1}

Details Multi-instantons in R^4 and Minimal Surfaces in R^{2,1} Multi-instantons in R^4 and Minimal Surfaces in R^{2,1}

2000-06-17

arxiv.org/abs/hep-th/0006135v1

JHEP 0008 (2000) 049

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1088/1126-6708/2000/08/049

It is known that self-duality equations for multi-instantons on a line in four dimensions are equivalent to minimal surface equations in three dimensional Minkowski space. We extend this equivalence beyond the equations of motion and show that topological number, instanton moduli space and anti-self-dual solutions have representations in terms of minimal surfaces. The issue of topological charge is quite subtle because the surfaces that appear are non-compact. This minimal surface/instanton correspondence allows us to define a metric on the configuration space of the gauge fields. We obtain the minimal surface representation of an instanton with arbitrary charge. The trivial vacuum and the BPST instanton as minimal surfaces are worked out in detail. BPS monopoles and the geodesics are also discussed.

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