Nahm dualities on the torus - a synthesis

We give a unified description of self-dual SU(2) gauge fields on tori of si ze l(t) X l(s)(3), based on a mixture of analytical and numerical methods u sing the Nahm transformation, extended to the case of twisted boundary cond itions. We show how torus calorons (l(t)/l(s) small) are Nahm dual to the t orus instantons (l(t)/l(s) large). Holonomies are dual to the locations of constituents, this duality becoming exact in the limiting cases l(s) or l(t ) --> infinity. Implications for the moduli spaces are discussed. (C) 2000 Elsevier Science B.V. All rights reserved.