Manuel Asorey

Departamento de Física Teórica, Universidad de Zaragoza

Nahm transform in $CP^n$ sigma models
There is a Fourier-Mukai 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. We have proved 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 topology of the moduli space of instantons based on a complete and explicit parametrization of all self-dual solutions on the two-dimensional torus. We also show that boundary of the space of regular instantons does coincide with the space of singular instantons.