The many facets of Nahm's duality transformation

by P. VAN BAAL (Leiden)

Tuesday 17 Aug 1999, 14:00 → 14:15 Europe/Zurich

TH Auditorium (CERN)

The Nahm transformation maps SU(N) self-dual gauge fields of charge k on a torus, to SU(k) self-dual gauge fields of charge N on the dual torus. It forms an involution that preserves metric and hyperKahler structure of the instanton moduli spaces. It can be put to practical use by observing that charge 1 instantons are mapped to an abelian problem, and that non-compact directions (infinite periods) lead to dimensional reduction on the dual torus. Intricate relations have been found, partly based on numerical studies and partly on analytic results, whose usefulness may extend beyond gauge theory applications. We give an overview over the results that have been obtained and the problems that still need to be resolved.