Nahm dualities on the torus - a synthesis

Abstract We give a unified description of self-dual SU(2) gauge fields on tori of size lt×ls3, 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→∞. Implications for the moduli spaces are discussed.