Constraining Maximally Supersymmetric Membrane Actions

Abstract

We study the recent construction of maximally supersymmetric field theory Lagrangians in three spacetime dimensions that are based on algebras with a triple product. Assuming that the algebra has a positive definite metric compatible with the triple product, we prove that the only non-trivial examples are either the well known case based on a four dimensional algebra or direct sums thereof.

11 pages, very minor changes. Reference added. Version to be published in JHEP

References in corpus (16)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Comments on Multiple M2-branes
• Comments on the Bagger-Lambert theory and multiple M2-branes
• M2 to D2
• Membranes on an Orbifold
• Selfdual strings and loop space Nahm equations
• M2-branes, 3-Lie Algebras and Plucker relations
• N = 8 Superconformal Chern--Simons Theories
• M2-branes on M-folds
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