Doubly Periodic Instantons and their Constituents

Using the Nahm transform we investigate doubly periodic charge one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as the locations of instanton core constituents. For a square torus this constituent picture is closely reflected in the action density. In rectangular tori with large aspect ratios the cores merge to form monopole-like objects. For particular values of the parameters the torus can be cut in half yielding two copies of a twisted charge 1/2 instanton. These findings are illustrated with plots of the action density within a two-dimensional slice containing the constituents.