Light-cone analysis of ungauged and topologically gauged BLG theories

TL;DR

This paper analyzes three-dimensional maximally superconformal BLG theories, both ungauged and topologically gauged, in the light-cone gauge, revealing their structure, superspace formulation, and interaction challenges.

Contribution

It provides a light-cone superspace formulation of BLG theories and explores the structure and interactions of topologically gauged versions, including supergravity couplings.

Findings

Ungauged BLG resembles N=4 super-Yang-Mills after gauge field elimination

Superspace formulation achieved up to quartic order, with interaction issues at sixth order

Topologically gauged BLG exhibits unique features and supergravity couplings

Abstract

We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory looks more conventional and, apart from the order of the interaction terms, resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given to quadratic and quartic order and some problems with constructing the sixth order interaction terms are discussed. In the topologically gauged case, we analyze the field equations related to the three Chern-Simons type terms of N=8 conformal supergravity and discuss some of the special features of this theory and its couplings to BLG.