Supermembrane with Non-Abelilan Gauging and Chern-Simons Quantization

TL;DR

This paper develops a framework for non-Abelian gaugings of supermembranes in eleven-dimensional supergravity, introducing a super Killing vector and demonstrating gauge coupling quantization linked to the topology of the gauge group.

Contribution

It extends supermembrane theory to include non-Abelian gauge symmetries with a novel super Killing vector and quantized coupling constants, broadening the understanding of membrane compactifications.

Findings

Introduced a super Killing vector for non-Abelian gauge groups.

Coupling constant quantization linked to a_3(G) topology.

Established a method using teleparallel superspace without local Lorentz covariance.

Abstract

We present non-Abelian gaugings of supermembrane for general isometries for compactifications from eleven-dimensions, starting with Abelian case as a guide. We introduce a super Killing vector in eleven-dimensional superspace for a non-Abelian group G associated with the compact space B for a general compactification, and couple it to a non-Abelian gauge field on the world-volume. As a technical tool, we use teleparallel superspace with no manifest local Lorentz covariance. Interestingly, the coupling constant is quantized for the non-Abelian group G, due to its generally non-trivial mapping \pi_3(G).