Asymptotically Free $\hat{U}(1)$ Kac-Moody Gauge Fields in $3+1$ dimensions

Abstract

$\hat{U}(1)$ Kac-Moody gauge fields have the infinite dimensional $\hat{U}(1)$ Kac-Moody group as their gauge group. The pure gauge sector, unlike the usual $U(1)$ Maxwell lagrangian, is nonlinear and nonlocal; the Euclidean theory is defined on a $d+1$-dimensional manifold ${\mathcal{R}}_d\times {\mathcal{S}}^1$ 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.

20 page Latex File. Figures in a separate uuencoded postscript file

References in corpus (2)

• Low Energy Dynamics of the Spinon-Gauge System
• Maximum temperature for an Ideal Gas of $\hat{U}(1)$ Kac-Moody Fermions

Cited by in corpus (1)

• (Supersymmetric) Kac-Moody Gauge Fields in 3+1 Dimensions