Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories

Understand

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.