Graviton and Gluon Scattering from First Principles

In this paper we study tree-level amplitudes from higher-dimensional operators, including F 3 operator of gauge theory, and R 2 , R 3 operators of gravity, in the Cachazo-He-Yuan formulation. As a generalization of the reduced Pfaffian in Yang-Mills theory, we find a new, gauge-invariant object that leads to gluon amplitudes with a single insertion of F 3 , and gravity amplitudes by Kawai-Lewellen-Tye relations. When reduced to four dimensions for given helicities, the new object vanishes for any solution of scattering equations on which the reduced Pfaffian is non-vanishing. This intriguing behavior in four dimensions explains the vanishing of graviton helicity amplitudes produced by the Gauss-Bonnet R 2 term, and provides a scattering-equation origin of the decomposition into self-dual and anti-self-dual parts for F 3 and R 3 amplitudes.

Section: Introduction and Motivationsmentioning

confidence: 92%

New formulas for amplitudes from higher-dimensional operators

Zhang

2017

“…We should perhaps note that Lagrangians with similar operators have previously been studied for phenomenological reasons in [13][14][15][16][17][18] and because the operators arise as corrections in the α expansion of bosonic open string theory [19][20][21]. It is however the specific theory introduced in [6] that interests us as it satisfies color-kinematics duality and gives conformal gravity through the double copy.…”

Section: (Df ) Theorymentioning

confidence: 99%

Ambitwistor formulations of R2 gravity and (DF)2 gauge theories

Azevedo

Engelund

2017

We consider D-dimensional amplitudes in R 2 gravities (conformal gravity in D = 4) and in the recently introduced (DF ) 2 gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the (DF ) 2 gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to D dimensions. The ambitwistor is also interpreted as a D-dimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another (DF ) 2 gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.

“…It was shown by Boels and Medina [7] that higher-point Einstein-Hilbert amplitudes can be obtained from the 3-point amplitude by imposing the symmetry and unitarity conditions. Furthermore this is the only amplitude (among the two possible ones that we found here) that corresponds to a constructible theory [5], and as predicted by the famous KLT relation between open and closed strings [24].…”

Section: Jhep12(2017)048mentioning

confidence: 99%

“…Benincasa and Cachazo used BCFW to investigate a class of "constructible" theories and found that there are no nontrivial amplitudes of different species of spin-2 particles or particles with spin larger than 2 among this class of theories, while a theory with a single kind of spin-2 particles is unique. Lately Boels and Medina [7] have obtained the threepoint amplitudes using the constraints of on-shell gauge invariance. Their results are expressed in terms of polarization tensors with the gauge transformations manifest; these have been done for polarization vectors and rank-2 polarization tensors, but not for general polarizations.…”

Section: Jhep12(2017)048mentioning

confidence: 99%

On-shell gauge invariant three-point amplitudes

Sun

Cheung

2017

Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches.Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field φ and an antisymmetric rank-2 tensor field A µν . Despite the well-known fact that in 4 dimensions rank-2 antisymmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.