Electromagnetic Self-Duality in a Lattice Model

Abstract

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 $eg=2\pi$. 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 $e\to 0$, fermion mass $\mu \to 0$, 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.

29 pages plain TeX, 2 PostScript figures included using psfig

References in corpus (4)

• Effects of Virtual Monopoles
• Monopole Percolation and The Universality Class of the Chiral Transition in Four Flavor Noncompact Lattice QED
• Spectroscopy, Equation Of State And Monopole Percolation In Lattice QED With Two Flavors
• Large N Lattice QED

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• Duality and scaling in 3-dimensional scalar electrodynamics
• The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction
• Screening and confinement in U(1)^{N-1} Abelian effective theories
• Chiral transition and monopole percolation in lattice scalar QED with quenched fermions