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

TL;DR

This paper develops a framework for constructing gauge and matter field Lagrangians using infinite-dimensional Kac-Moody algebras, introducing novel nonlinear interactions and extending to supersymmetric cases in four dimensions.

Contribution

It introduces a continuum regularization method for Kac-Moody gauge theories and derives new Yang-Mills and Chern-Simons Lagrangians, including supersymmetric extensions.

Findings

Derived new nonlinear interactions in Kac-Moody gauge theories

Extended the framework to supersymmetric gauge fields in 4D

Presented continuum regularization as a tool for infinite-dimensional gauge theories

Abstract

Lagrangians for gauge fields and matter fields can be constructed from the infinite dimensional Kac-Moody algebra and group. A continuum regularization is used to obtain such generic lagrangians, which contain new nonlinear and asymmetric interactions not present in gauge theories based on compact Lie groups. This technique is applied to deriving the Yang-Mills and Chern-Simons lagrangians for the Kac-Moody case. The extension of this method to D=4, N=(1/2,0) supersymmetric Kac-Moody gauge fields is also made.