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$ \hat {U}(1)$ Kac-Moody gauge fields have the infinite dimensional $\hat{U}(1)$ Kac-Moody group as their gauge group. The pure gauge sector, unlikethe usual $U(1)$ Maxwell lagrangian, is nonlinear and nonlocal; the Euclideantheory is defined on a $d+1$-dimensional manifold $ {\cal{R}}_d \times{\cal{S}}^1 $ and hence is also asymmetric. We quantize this theory using thebackground field method and examine its renormalizability at one-loop byanalyzing all the relevant diagrams. We find that, for a suitable choice of thegauge field propagators, this theory is one-loop renormalizable in $3+1$dimensions. This pure abelian Kac-Moody gauge theory in $3+1$ dimensions hasonly one running coupling constant and the theory is asymptotically free. Whenfermions are added the number of independent couplings increases and a richerstructure is obtained. Finally, we note some features of the theory whichsuggest its possible relevance to the study of anisotropic condensed mattersystems, in particular that of high-temperature superconductors.Comment: 20 page Latex File. Figures in a separate uuencoded postscript fil

Asymptotically free Û(1) Kac-Moody gauge fields in 3 + 1 dimensions