Nahm Transform and Moduli Spaces of CPN-Models on the Torus

✍ Scribed by M. Aguado; M. Asorey; A. Wipf

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 404 KB
• Volume: 298
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2002.6237

✦ Synopsis

There is a Nahm transform for 2-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 CP N instantons. This fact establishes a significative difference between 4-D gauge theories and CP N 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 2-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 CP N sigma models.