Classification of the BPS states in Bagger-Lambert Theory

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.

28+1 pages, No figure; v2 Sec.3.3 slightly expanded, typos fixed; v3 some comments added, to appear in JHEP

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• M5 brane from mass deformed BLG theory
• Three-algebra for supermembrane and two-algebra for superstring
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• BPS Vortices, $Q$-balls, and $Q$-vortices in $\mathcal{N}=6$} Chern-Simons Matter Theory
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