Nahm dualities on the torus – a synthesis

Abstract

We give a unified description of self-dual SU(2) gauge fields on tori of size l t × l s 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 ( l t / l s small) are Nahm dual to the torus 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 →∞. Implications for the moduli spaces are discussed.