Lorentzian Lie 3-algebras and their Bagger-Lambert moduli space

TL;DR

This paper classifies Lorentzian Lie 3-algebras, explores their moduli space in Bagger-Lambert theory, and links certain branches to symmetric spaces, revealing models with N^{3/2} scaling behavior.

Contribution

It provides a complete classification of Lorentzian Lie 3-algebras and analyzes their moduli space, connecting it to symmetric spaces and specific scaling properties.

Findings

Classified indecomposable Lorentzian Lie 3-algebras.

Established correspondence between moduli space branches and symmetric spaces.

Identified models with N^{3/2} scaling behavior.

Abstract

We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical vacua of the Bagger-Lambert theory corresponding to these Lie 3-algebras. We establish a one-to-one correspondence between one branch of the moduli space and compact riemannian symmetric spaces. We analyse the asymptotic behaviour of the moduli space and identify a large class of models with moduli branches exhibiting the desired N^{3/2} behaviour.