Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Israel.
Indian Institute of Science Education and Research, Homi Bhabha Road, Pashan, Pune 411 008, India.
Phys Rev Lett. 2018 Oct 19;121(16):161601. doi: 10.1103/PhysRevLett.121.161601.
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.
我们证明了 Britto-Cachazo-Feng-Witten（BCFW）递归关系可以用于计算 U(N) N=2 Chern-Simons（CS）理论与基本表示中的物质耦合的所有树级散射振幅，而无需使用 2→2 散射振幅。作为副产品，我们还获得了 CS 理论与正则费米子耦合的递归关系，尽管在这种情况下标准 BCFW 变形没有良好的渐近行为。此外，在大 N 下，正如一些作者之前的工作所做的那样，可以精确计算 't Hooft 耦合的所有阶次的 2→2 散射。特别是，对于 N=2 理论，已经表明除了任意子通道[K. Inbasekar 等人，J. High Energy Phys. 10（2015）17610.1007/JHEP10(2015)176]外，2→2 散射在所有阶次都是精确的，在该通道中，它被 't Hooft 耦合的简单函数正则化。这表明，在大 N 下，可能有可能计算任意高阶散射振幅的全环精确结果。
