Dual Superconformal Symmetry of ${\cal N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$

TL;DR

This paper demonstrates that the tree-level 2-to-2 scattering amplitude in 3d ${ m N}=2$ Chern-Simons theory with fundamental matter exhibits dual superconformal symmetry, which remains exact at all loops, unlike in more supersymmetric theories.

Contribution

It establishes dual superconformal invariance at all loops in a less supersymmetric ${ m N}=2$ Chern-Simons theory, and explores how this symmetry constrains the amplitude's form.

Findings

Dual superconformal symmetry is exact at all loops in the theory.

The symmetry completely determines the momentum dependence of the amplitude.

Coupling dependence remains unfixed by dual superconformal symmetry alone.

Abstract

Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like ${\cal N}=4$ SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level $2\to 2$ scattering amplitude in the 3d ${\cal N}=2$ Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the 't Hooft large $N$ limit, the $2\to 2$ scattering amplitude in this theory has been shown to be tree-level exact in non-anyonic channels, while having only an overall multiplicative coupling dependent renormalisation in the anyonic channel. Therefore, the dual superconformal symmetry that we demonstrate in this paper is all loop exact. This is unlike the previously studied highly supersymmetric theories where dual superconformal symmetry is anomalous at loop levels. Furthermore, we reverse the argument to study the extent to which dual superconformal invariance fixes the scattering amplitude in an ${\cal N}=2$ supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the $2\to2$ amplitude, while the coupling constant dependence remain unfixed. Further, we use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling dependence of scattering amplitude.