Nahm dualities on the torus - a synthesis

We give a unified description of self-dual SU(2) gauge fields on tori of size lt x ls^3 based on a mixture of analytical and numerical methods using the Nahm transformation, extended to the case of twisted boundary conditions. We show how torus calorons (lt/ls small) are Nahm dual to the torus instantons (lt/ls large). Holonomies are dual to the locations of constituents, this duality becoming exact in the limiting cases ls or lt --> infinity. Implications for the moduli spaces are discussed.Comment: Latex, 22 pages, 8 figures in 11 postscript file

Comments on the Instanton Size Distribution

By studying the non-linear effects of overlapping instanton pairs we address difficulties in the identification of instanton distributions when the average instanton size is comparable to the average distance. For the exact charge two solution, we study how its parametrisation relates to a description in terms of individual instantons. There exist two dual sets of parameters describing the same charge two instanton solution. This duality implies the existence of a minimal separation between two instantons. Conventionally used lattice instanton finder algorithms based on the assumption of diluteness tend to underestimate instanton sizes. Finally we numerically confirm this for realistic parameters of the instanton liquid. The effect is enhanced by parallel orientation in group space.Comment: LaTeX, 15 pages, 3 figure