Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories
arXiv:0908.2618 · doi:10.1007/JHEP08(2010)077
Abstract
We define a 3-algebra with structure constants being symmetric in the first two indices. We also introduce an invariant anti-symmetric tensor into this 3-algebra and call it a symplectic 3-algebra. The general N=5 superconformal Chern-Simons-matter (CSM) theory with SO(5) R-symmetry in three dimensions is constructed by using this algebraic structure. We demonstrate that the supersymmetry can be enhanced to N=6 if the sympelctic 3-algebra and the fields are decomposed in a proper fashion. By specifying the 3-brackets, some presently known N=5, 6 superconformal theories are described in terms of this unified 3-algebraic framework. These include the N=5, Sp(2N) X O(M) CSM theory with SO(5) R-symmetry , the N=6, Sp(2N) X U(1) CSM theory with SU(4) R-symmetry, as well as the ABJM theory as a special case of U(M) X U(N) theory with SU(4) R-symmetry.
31 pages, minor changes, final results remain the same
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- Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations
- Exceptional geometry and Borcherds superalgebras
- Monopoles, three-algebras and ABJM theories with supersymmetry
- M-Theory and Maximally Supersymmetric Gauge Theories
- M5 brane from mass deformed BLG theory
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- Supersymmetric solutions from N=5 gauged supergravity
- Unifying N=5 and N=6
- 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
- Construction of New D=3, N=4 Quiver Gauge 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
- OSp(5|4) Superconformal Symmetry of N=5 Chern-Simons Theory
- Superconformal Chern-Simons theories beyond leading order
- Multiple M-branes and 3-algebras
- OSp(4|4) superconformal currents in three-dimensional N=4 Chern-Simons quiver gauge theories