Superspace formulation in a three-algebra approach to D=3, N=4, 5 superconformal Chern-Simons matter theories

Journal Article · Mon Nov 15 04:00:00 EST 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.106012· OSTI ID:21503694

Famin, Chen; Yongshi, Wu ^[1]

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1. Department of Physics and Astronomy, University of Utah Salt Lake City, Utah 84112-0830 (United States)

We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.

• OSTI ID: 21503694
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 82; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
FIELD THEORIES
LIE GROUPS
MATHEMATICS
MATTER
MULTIPLETS
POTENTIALS
QUANTUM FIELD THEORY
SHELLS
SUPERMULTIPLETS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
TENSORS
TRANSFORMATIONS