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

TL;DR

This paper demonstrates that BCFW recursion relations can compute all tree-level scattering amplitudes in certain Chern-Simons theories with fundamental matter, revealing exact results at large N and potential for all-loop calculations.

Contribution

It introduces a method to derive all tree-level amplitudes in Chern-Simons theories using BCFW recursion, including cases with regular fermions, and discusses exact large N results.

Findings

BCFW recursion applies to all tree-level amplitudes in these theories.

2→2 scattering is exact at large N, except in the anyonic channel.

Potential for computing all-loop exact higher-point amplitudes at large N.

Abstract

We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be used to compute all tree level scattering amplitudes in terms of $2\rightarrow2$ 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 $N$, $2\rightarrow 2$ 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 $2\rightarrow 2$ 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 $N$.