N=8 superconformal gauge theories and M2 branes

Abstract

Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R^8)^N/S_N. These properties are expected for the field theory living on a stack of M2 branes.

14 pages, no figures

References in corpus (13)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Modeling Multiple M2's
• Comments on the Bagger-Lambert theory and multiple M2-branes
• M2 to D2
• Membranes on an Orbifold
• M2-branes, 3-Lie Algebras and Plucker relations
• N = 8 Superconformal Chern--Simons Theories
• Mass-Deformed Bagger-Lambert Theory and its BPS Objects
• Bagger-Lambert Theory for General Lie Algebras
• Multiple M2-branes and the Embedding Tensor
• Aspects of Multiple Membranes
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories

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