Multiply periodic instantons

by Chris FORD (Leiden University)

Thursday 6 Dec 2001, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

It is a long standing problem to construct periodic Yang-Mills instantons. Mathematically speaking we seek instantons on a torus Tⁿ x R^(4-n), n = 1, 2, 3 or 4. For n > 1, no explicit (non-Abelian) solutions have been found. It is known that T⁴ instantons possess a remarkable property known as Nahm duality whereby SU(N) instantons with topological charge k are related to SU(k) charge N instantons on the dual torus (defined by inverting the four periods). Unfortunately, there does not seem to be a way to use this duality to construct instantons on T⁴. Simply put, it maps one hard problem to another. When n < 4 the situation is different, and in recent years there has been much activity in this area. In particular, new caloron solutions (n = 1) have been extracted and intensively studied. In this talk I will give a basic introduction to Nahm duality, and outline some recent work dealing with the n = 2 case (doubly periodic instantons).