Eur. Phys. J. C 69, 305-314 (2010)
https://doi.org/10.1140/epjc/s10052-010-1385-4

Symplectic three-algebra and , Sp(2N)×U(1) superconformal Chern–Simons-matter theory

Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, 84112-0830, USA

fchen@physics.utah.edu

Received: 17 March 2010
Revised: 8 May 2010
Published online: 21 July 2010

Abstract

We introduce an antisymmetric metric into a 3-algebra and call it a symplectic 3-algebra. The , Sp(2N)×U(1) superconformal Chern–Simons-matter theory with SU(4) R-symmetry in three dimensions is constructed by specifying the 3-brackets in a symplectic 3-algebra. We also demonstrate that the , U(M)×U(N) theory can be recast into this symplectic 3-algebraic framework.