Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations

Abstract

In this work we present 3-algebraic constructions and representations for three-dimensional N = 5 supersymmetric Chern-Simons theories, and show how they relate to theories with additional supersymmetries. The N = 5 structure constants give theories with Sp(2N) \times SO(M) gauge symmetry, as well as more exotic symmetries known from gauged supergravity. We find explicit lifts from N = 6 to 8, and N = 5 to 6 and 8, for appropriate gauge groups.

arXiv comment23 pages. Published version. References corrected

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Cited by in corpus (19)

• n-ary algebras: a review with applications
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Multiple Membranes in M-theory
• The tensor hierarchy algebra
• Exceptional geometry and Borcherds superalgebras
• Monopoles, three-algebras and ABJM theories with $\mathbb{N}=5,6,8$ supersymmetry
• M-Theory and Maximally Supersymmetric Gauge Theories
• Lessons from M2's and Hopes for M5's
• Supersymmetric solutions from N=5 gauged supergravity
• Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories
• Degenerations of Filippov algebras
• Supersymmetric solutions from N=6 gauged supergravity
• N=5 three-algebras and 5-graded Lie superalgebras
• Superalgebra Realization of the 3-algebras in N=6, 8 Chern-Simons-matter Theories
• Fusion of Superalgebras and D=3, N=4 Quiver Gauge Theories
• Covariantly Constant Curvature Tensors and D=3, N=4, 5, 8 Chern-Simons Matter Theories
• Algebraic vs physical N=6 3-algebras
• Multiple M-branes and 3-algebras
• Superconformal Chern-Simons theories beyond leading order