Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like 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 → 2 scattering amplitude in the 3d N = 2 Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the ’t Hooft large N limit, the 2 → 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 N = 2 supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the 2 → 2 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.
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Article funded by SCOAP3.
The work of KI was supported in part by a center of excellence supported by the Israel Science Foundation (grant number 1989/14), the US-Israel binational fund (BSF) grant number 2012383 and the Germany Israel bi-national fund GIF grant number I-244-303.7-2013. The work of P.N. and R.S. was supported partly by Infosys Endowment for the study of the Quantum Structure of Space Time. P.N. also acknowledges support from the College of Arts and Sciences of the University of Kentucky and Indo-Israel grant of S. Minwalla. M acknowledges support from a CSIR NET fellowship. TN acknowledges support from a UGC NET fellowship.
Inbasekar, Karthik; Jain, Sachin; Majumdar, Sucheta; Nayak, Pranjal; Neogi, Turmoli; Sinha, Ritam; Sharma, Tarun; and Umesh, V., "Dual Superconformal Symmetry of N = 2 Chern-Simons Theory with Fundamental Matter at Large N" (2019). Physics and Astronomy Faculty Publications. 663.