Nahm Transform and Moduli Spaces of CPn Models on the Torus

Details Nahm Transform and Moduli Spaces of CPn Models on the Torus Nahm Transform and Moduli Spaces of CPn Models on the Torus

2001-07-30

arxiv.org/abs/hep-th/0107258v1

Annals Phys. 298 (2002) 2-23

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, 5 eps-figures

Scientific paper

10.1006/aphy.2002.6237

There is a Nahm transform for two-dimensional gauge fields which establishes a one-to-one correspondence between the orbit space of U(N) gauge fields with topological charge k defined on a torus and that of U(k) gauge fields with charge N on the dual torus. The main result of this paper is to show that a similar duality transform cannot exist for CPn instantons. This fact establishes a significative difference between 4-D gauge theories and CPn models. The result follows from the global analysis of the moduli space of instantons based on a complete and explicit parametrization of all self-dual solutions on the two-dimensional torus. The boundary of the space of regular instantons is shown to coincide with the space of singular instantons. This identification provides a new approach to analyzing the role of overlapping instantons in the infrared sector of CPn sigma models.

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