We explore the possibilities for constructing Lagrangian descriptions of threedimensional superconformal classical gauge theories that contain a Chernâ€“Simons term, but no kinetic term, for the gaugeâ€¦ (More)

The Bagger-Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimpleâ€¦ (More)

We examine the three-dimensional N = 6 superconformal Chern-Simons theory with U(N) Ã— U(N) gauge symmetry, which was recently constructed by Aharony, Bergman, Jafferis, and Maldacena (ABJM). Using aâ€¦ (More)

We develop ambitwistor string theories for four dimensions to obtain new formulas for tree-level gauge and gravity amplitudes with arbitrary amounts of supersymmetry. Ambitwistor space is the spaceâ€¦ (More)

We use supertwistor space to construct scattering amplitudes of maximal superconformal theories in three and six dimensions. In both cases, the constraints of superconformal invariance andâ€¦ (More)

We demonstrate that the four and six-point tree-level amplitudes of N = 6 superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace toâ€¦ (More)