Classification of the BPS states in Bagger-Lambert Theory

TL;DR

This paper classifies BPS configurations in the Bagger-Lambert multiple M2-brane theory, revealing three types of equations with different symmetry properties and algebraic structures related to division algebras.

Contribution

It provides a group theoretical classification of BPS states in the Bagger-Lambert theory, identifying three distinct types with specific symmetry and algebraic features.

Findings

Identified three types of BPS equations with different symmetry invariances.

Connected BPS equations to division algebra structures: octonion, quaternion, complex.

Extended Nahm equations to eleven-dimensional generalizations.

Abstract

We classify, in a group theoretical manner, the BPS configurations in the multiple M2-brane theory recently proposed by Bagger and Lambert. We present three types of BPS equations preserving various fractions of supersymmetries: in the first type we have constant fields and the interactions are purely algebraic in nature; in the second type the equations are invariant under spatial rotation SO(2), and the fields can be time-dependent; in the third class the equations are invariant under boost SO(1,1) and provide the eleven-dimensional generalizations of the Nahm equations. The BPS equations for different number of supersymmetries exhibit the division algebra structures: octonion, quarternion or complex.