Alephnull-Extended Supersymmetric Chern-Simons Theory for Arbitrary Gauge Groups

TL;DR

This paper introduces a novel class of three-dimensional supersymmetric non-Abelian Chern-Simons theories with an arbitrary number of supersymmetries equal to the gauge group's dimension, highlighting their potential links to M-theory.

Contribution

It constructs alephnull-extended supersymmetric Chern-Simons models for any gauge group, with local supersymmetry and quantized coupling constants due to topological considerations.

Findings

Supersymmetry parameter in the adjoint leads to local supersymmetry.

Coupling constant quantization when _3(G) = Z.

Potential connections to M-theory.

Abstract

We present a model of supersymmetric non-Abelian Chern-Simons theories in three-dimensions with arbitrarily many supersymmetries, called alephnull-extended supersymmetry. The number of supersymmetry N equals the dimensionality of any non-Abelian gauge group G as N = dim G. Due to the supersymmetry parameter in the adjoint representation of a local gauge group G, supersymmetry has to be local. The minimal coupling constant is to be quantized, when the homotopy mapping is nontrivial: \pi_3(G) = Z. Our results indicate that there is still a lot of freedom to be explored for Chern-Simons type theories in three dimensions, possibly related to M-theory.