All Tree Level Scattering Amplitudes in Chern-Simons Theories with Fundamental Matter

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) 17610.1007/JHEP10(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.