Dual Superconformal Symmetry of N=6 Chern-Simons Theory

TL;DR

This work shows that four- and six-point tree amplitudes in ABJM theory exhibit dual superconformal symmetry under the supergroup $OSp(6|4)$ when the dual space is extended by three new Grassmann-even coordinates $y^{AB}$ that encode R-symmetry directions. The dual conformal boost $K^{ ho heta}$ is demonstrated to be equivalent to the level-1 Yangian generator $J^{(1) ho heta}$ on on-shell amplitudes, linking dual symmetry to integrability. The $y^{AB}$ coordinates provide a geometric interpretation tied to the half-coset structure of SU(4)/U(3)_+, and they enable consistent dual supersymmetry generators that commute with the hyperplane constraints. The authors discuss loop-level implications, predicting vanishing one-loop four-point amplitudes by parity and outlining the structure of two-loop contributions, and offer directions for exploring Wilson-loop/ amplitude dualities and higher-point generalizations.

Abstract

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 to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some implications of dual conformal symmetry for loop-level amplitudes.

Figures (2)

• Figure 1: Summary of superspace for $\mathcal{N}=6$ Chern-Simons theory. In section 6, we will show that the dual space requires three additional Grassman-even coordinates.
• Figure 2: Possible one-loop four-point integrals.