Related papers: Taming Tree Amplitudes In General Relativity
Continuing the study of boundary BCFW recursion relation of tree level amplitudes initiated in \cite{Feng:2009ei}, we consider boundary contributions coming from fermion pair deformation. We present the general strategy for these boundary…
These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight…
The relationship between certain geometric objects called polytopes and scattering amplitudes has revealed deep structures in QFTs. It has been developed in great depth at the tree- and loop-level amplitudes in $\mathcal{N}=4~\text{SYM}$…
In this article, we analyze the boundary behaviors of pure Yang-Mills amplitudes under adjacent and non adjacent BCFW shifts in Feynman gauge. We introduce reduced vertexes for Yang-Mills fields, prove that these reduced vertexes are…
Using recursion methods similar to those of Britto, Cachazo, Feng and Witten (BCFW) a direct proof of the CSW rules for computing tree-level gluon amplitudes is given.
We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for…
We review two novel techniques used to calculate tree-level scattering amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the MHV diagrams, we consider applications to tree-level amplitudes and focus in particular…
We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z…
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…
The tree-level scattering amplitudes of general relativity encode the full non-linearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative…
This article revisits and elaborates the significant role of positive geometry of momentum twistor Grassmannian for planar N=4 SYM scattering amplitudes. First we establish the fundamentals of positive Grassmannian geometry for tree…
We give a new formalism for pure gauge-theoretic scattering at tree-amplitude level. We first describe a generalization of the Britto-Cachazo-Feng recursion relation in which a significant restriction is removed. We then use twistor…
This article studies methods to obtain relations for scattering amplitudes at the loop level, with concrete examples at one loop. These methods originate in the analysis of large so-called Britto-Cachazo-Feng-Witten shifts of tree level…
This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we expose analytic properties of gauge-boson…
We study the application of non-trivial relations between gravity tree amplitudes, the bonus relations, to all tree-level amplitudes in N=8 supergravity. We show that the relations can be used to simplify explicit formulae of supergravity…
In the gauge-theoretic formulation of gravity the cubic vertex becomes simple enough for some graviton scattering amplitudes to be computed using Berends-Giele-type recursion relations. We present such a computation for the current with all…
It is shown how tree-level multi-gluon helicity amplitudes with an arbitrary number of off-shell external gluons can be calculated via BCFW recursion. Compact expressions for helicity amplitudes for scattering processes of three and four…
One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes, if working in the light cone gauge. As shown in recent works…
We derive general tree-level recursion relations for amplitudes which include massive propagating particles. As an illustration, we apply these recursion relations to scattering amplitudes of gluons coupled to massive scalars. We provide…
In this article a first step is made towards the extension of Britto-Cachazo-Feng-Witten (BCFW) tree level on-shell recursion relations to integrands and integrals of scattering amplitudes to arbitrary loop order. Surprisingly, it is shown…