We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be used to compute all tree level scattering amplitudes in terms of 2 → 2 scattering amplitude in U(N) 𝒩 = 2 Chern-Simons (CS) theory coupled to matter in the fundamental representation. As a by-product, we also obtain a recursion relation for the CS theory coupled to regular fermions, even though in this case standard BCFW deformations do not have a good asymptotic behavior. Moreover, at large N, 2 → 2 scattering can be computed exactly to all orders in ’t Hooft coupling as was done in earlier works by some of the authors. In particular, for 𝒩 = 2 theory, it was shown that 2 → 2 scattering is tree level exact to all orders except in the anyonic channel [K. Inbasekar et al., J. High Energy Phys. 10 (2015) 176], where it gets renormalized by a simple function of ’t Hooft coupling. This suggests that it may be possible to compute the all loop exact result for arbitrary higher-point scattering amplitudes at large N.
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The work of K. I. was supported in part by a center of excellence supported by the Israel Science Foundation (Grant No. 1989/14), the US-Israel binational fund (BSF) Grant No. 2012383, and the Germany Israel binational fund GIF Grant No. I-244-303.7-2013. S. J. would like to thank TIFR for hospitality at various stages of the work. Some part of the work in this Letter was completed while S. J. was a postdoctoral candidate at Cornell and his research was supported by Grant No. 488643 from the Simons Foundation. The work of P. N. is supported partly by Infosys Endowment for the study of the Quantum Structure of Space Time and Indo-Israel grant of S. Minwalla; and partly by the College of Arts and Sciences of the University of Kentucky.
Inbasekar, Karthik; Jain, Sachin; Nayak, Pranjal; and Umesh, V., "All Tree Level Scattering Amplitudes in Chern-Simons Theories with Fundamental Matter" (2018). Physics and Astronomy Faculty Publications. 611.