Abstract
We consider D-dimensional amplitudes in R2 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.
Highlights
We show that these theories can be given a straightforward interpretation in terms of ambitwistor strings
As part of our ambitwistor investigation, we discover another (DF )2 gauge theory containing a photon that couples to Einstein gravity
Conformal supergravity can be related to Einstein gravity in asymptotically de Sitter space [11] and its U(1) anomaly can be used to study the similar anomaly in Poincare supergravity [12]
Summary
It is our goal to express the amplitudes of the theory described in section 2 in the CHY formulation. The amplitudes of several quite different theories can be written in the following form in D dimensions: An = ign−2. The prime on the product sign means that three of the delta function are left out: j=i pi · pj σij This is necessary as the scattering equations are SL(2, C) invariant. In order to get Yang-Mills amplitudes, one can make the following choices for the left and right integrand: Tr (T aβ(1) T aβ(2) · · · T ) aβ(n). If one instead is interested in the amplitudes of Einstein gravity, one can choose both the left and the right integrand to be given by reduced Pfaffians: IL = Pf Mn,. One will end up with the amplitudes of a bi-adjoint scalar
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