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

Abstract

Û( l ) Kac-Moody gauge fields have the infinite dimensional Û( 1 ) Kac-Moody group as their gauge group. The pure gauge sector, unlike the usual U(l) Maxwell Lagrangian, is nonlinear and nonlocal; the Euclidean theory.is defined on a (d+ l)-dimensional manifold Rd×Sl 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 Û( 1 ) 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 suseest its possible relevance to the studv of anisotrooic condensed matter svstems, in particular, that of high-temperature superconductors. © 1996 The American Physical Society.