Abstract
We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only $\dlog$-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for $\N=8$ supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum, poles at infinity are present and loop amplitudes show special behavior on certain collinear cuts. We demonstrate on 1-loop and 2-loop examples that the behavior on collinear cuts is a highly non-trivial property which requires cancellations between all terms contributing to the amplitude.
Highlights
Background material onGrassmannian formulation of on-shell diagramsWithin the field of scattering amplitudes, a great number of developments in the last decade or so are based on powerful on-shell methods [2,3,4,5,6,7,8]
We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs
In this paper we studied on-shell diagrams in gravity theories
Summary
Within the field of scattering amplitudes, a great number of developments in the last decade or so are based on powerful on-shell methods [2,3,4,5,6,7,8]. In the traditional picture of Quantum Field Theory, locality and unitarity dictate the form and locations of all these residues They arise in kinematic regions where either internal particles or sums of external particles become on-shell. The fundamental cut is the well-known unitarity cut [57, 58] depicted on the left hand side of (2.1) Iterating these cuts one can calculate multi-dimensional residues by setting an increasing number of propagators to zero. This is known in the literature as generalized unitarity [4,5,6] and an example is given on the right hand side of (2.1). In this scenario we talk about on-shell diagrams [31]
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