Abstract
We present a new formula for all single trace tree amplitudes in four dimensional super Yang-Mills coupled to Einstein supergravity. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization and sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.
Highlights
We present a new formula for all single trace tree amplitudes in four dimensional super Yang-Mills coupled to Einstein supergravity
We have presented a new formula for all single trace tree amplitudes in supersymmetric Einstein Yang-Mills theory in four dimensions, written in terms of on-shell superspace
In the purely gravitational sector, the formula reduces to the representation of amplitudes given in [11, 16]
Summary
Before describing our formula, we first point out several ab initio constraints which any purported formula for sEYM must obey. In the purely gravitational sector this is the usual κn−2 factor associated with (the Euler character of) a gravitational tree graph, while if there are no external gravitons and only a single colour trace, we find κ0 as expected for the conformally invariant Yang-Mills answer. A final constraint is given by a rather curious observation about the tree amplitudes of sEYM theory in four dimensions: every colour trace of external gluons must contain at least one gluon of each helicity.. Amplitudes for individual helicity components of the supermultiplets are read off by expanding the exponential and extracting those terms of appropriate degree in the Grassmann variables Note that both (2.2) and (2.9) are manifestly parity symmetric
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