Instanton Moduli for T**3xR

Abstract

We review the specific problems that arise when studying instantons on a torus. We discuss how the Nahm transformation shows that no exact charge one instanton on T**4 can exist. However, taking one of the directions (the time) to infinity, it can be shown that vacuum to vacuum tunnelling solutions exist. A precise description of the moduli space for T**3xR, studied numerically using lattice techniques, remains an interesting open problem. New is an explicit application of the Nahm transformation to (anti-)selfdual constant curvature solutions on T**4 and a discussion of its properties relevant to instantons on T**3xR.Comment: 12p with 3 figs, uufiles -gz format. Talk at the 29th Int. Symp. on the Theory of Elem. Part., Buckow, 29 Aug.-2 Sept., 1995