Electromagnetic Self - Duality in a Lattice Model

We formulate a Euclidean lattice theory of interacting elementary spin-half electric and magnetic charges, which we refer to as electrons and magnetic monopoles respectively. The model uses the polymer representation of the fermion determinant , and exhibits a self-dual symmetry provided electric charge e and magnetic charge g obey the minimal Dirac quantisation condition eg = 2π. In a hopping parameter expansion at lowest order, we show that virtual electron and monopole loops contribute radiative corrections of opposite sign to the photon propagator. We argue that in the limit e → 0, fermion mass µ → 0, the model describes QED together with strongly interacting monopoles whose chiral symmetry is spontaneously broken. Prospects for the existence of an interacting continuum limit at the self-dual point e = g are discussed.