Lorentz-Covariant Non-Abelian Gauging of Supermembrane

TL;DR

This paper develops a Lorentz-covariant non-Abelian gauging framework for supermembranes, enabling consistent compactification from eleven dimensions to lower-dimensional spacetimes with non-Abelian gauge symmetries.

Contribution

It introduces a Lorentz-covariant formulation of non-Abelian gauging for supermembranes, extending previous teleparallel approaches to include manifest Lorentz covariance.

Findings

Formulation applicable to various compactifications such as M_{11} o S^{11-D} imes M_D

Inclusion of Killing supervector with adjoint index for non-Abelian gauge group

Enables consistent supermembrane gauging with Lorentz covariance

Abstract

We perform the Lorentz-covariant non-Abelian gauging of supermembrane (M-2 brane) action. This is a generalization of our previous work based on teleparallel formulation, in which Lorentz covariance was not manifest. We introduce the Killing supervector \xi^{A I} with the adjoint index I for a non-Abelian gauge group H. This formulation is applicable to the compactification of supermembrane from eleven dimensions into D dimensions, such as H = SO(11-D) for the compactification M_{11} \to S^{11-D} \times M_D (1\le D \le 9).