Asymptotically Free U(1) Kac-Moody Gauge Fields in 3+1 dimensions

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U(1) Kac-Moody gauge fields have the infinite dimensional U(1) Kac-Moody group as their gauge group. The pure gauge sector, unlike the usual U(1) Maxwell lagrangian, is nonlinear and nonlocal; the Euclidean theory is defined on a d+1-dimensional manifold Rd × S¹ and hence is also asymmetric. We quantize this theory using the background field method and examine its renormalizability at one-loop by analyzing all the relevant diagrams. We find that, for a suitable choice of the gauge field propagators, this theory is one-loop renormalizable in 3+1 dimensions. This pure abelian Kac-Moody gauge theory in 3+1 dimensions has only one running coupling constant and the theory is asymptotically free. When fermions are added the number of independent couplings increases and a richer structure is obtained. Finally, we note some features of the theory which suggest its possible relevance to the study of anisotropic condensed matter systems, in particular that of high-temperature superconductors.