Abstract
We argue that the scattering of gravitons in ordinary Einstein gravity possesses a hidden conformal symmetry at tree level in any number of dimensions. The presence of this conformal symmetry is indicated by the dilaton soft theorem in string theory, and it is reminiscent of the conformal invariance of gluon tree-level amplitudes in four dimensions. To motivate the underlying prescription, we demonstrate that formulating the conformal symmetry of gluon amplitudes in terms of momenta and polarization vectors requires manifest reversal and cyclic symmetry. Similarly, our formulation of the conformal symmetry of graviton amplitudes relies on a manifestly permutation symmetric form of the amplitude function.
Highlights
We argue that the scattering of gravitons in ordinary Einstein gravity possesses a hidden conformal symmetry at tree level in any number of dimensions
The presence of this conformal symmetry is indicated by the dilaton soft theorem in string theory, and it is reminiscent of the conformal invariance of gluon tree-level amplitudes in four dimensions
This is a consequence of the classical conformal symmetry of the Yang-Mills action, the conformal symmetry of gluon tree-amplitudes was first fomulated by Witten [4], who used an elegant representation of the conformal generators in spinor-helicity and twistor variables
Summary
When acting on δ-stripped amplitudes, it is useful to rewrite the conformal generators in terms of differential operators of the Lorentz invariant kinematical variables, ki · kj, ki · j and i · j, for i = j, by use of the chain rule, see appendix A for explicit expressions. We notice that such differential operators were considered recently in [28] to describe relations among amplitudes of different theories
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