All tree level scattering amplitudes in Chern-Simons theories with fundamental matter

Abstract

We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be used to compute all tree level scattering amplitudes in terms of $2\to 2$ scattering amplitude in $U(N)$ $\mathcal{N}=2$ Chern-Simons (CS) theory coupled to matter in fundamental representation. As a byproduct, 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 behaviour. Moreover at large $N$, $2\to 2$ 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 $\mathcal{N}=2$ theory, it was shown that $2\to 2$ scattering is tree level exact to all orders except in the anyonic channel arXiv:1505.06571, 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 $N$.

arXiv commentRevTEX 4.1, 5 pages+6 Appendices, 7 figures; V2 Published version

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• Mass-deformed $\mathcal{N}=3$ Supersymmetric Chern-Simons-Matter Theory
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• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter