Abstract
We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.
Highlights
Recent progress in the understanding of scattering amplitudes has revealed many novel mathematical structures that are hidden from the standard Lagrangian approach
In general, at higher points, the KLT formula [39, 40] will not be able to reproduce the wide range of gravitational interactions that can be obtained from the double copy of diagrams satisfying the fundamental color-kinematics duality
We propose to use the fact that multiplets X and X appear in the product (3.2) of the adjoint vectors and as the fundamental matter double copy in eqs. (3.1b) and (3.1c)
Summary
Recent progress in the understanding of scattering amplitudes has revealed many novel mathematical structures that are hidden from the standard Lagrangian approach. We eliminate the discussed limitations and formulate a double-copy prescription for amplitude integrands in Einstein gravity, pure supergravity theories, and supergravities with tunable non-self-interacting matter.. We eliminate the discussed limitations and formulate a double-copy prescription for amplitude integrands in Einstein gravity, pure supergravity theories, and supergravities with tunable non-self-interacting matter.1 This is achieved by introducing the color-kinematics duality to gauge theories with matter fields in the fundamental rep-. Once we obtain the tools to correctly subtract unwanted matter from loops, we can reverse the procedure and instead add more matter, introducing tunable parameters to count the number of matter states This generalization has a simple intuitive understanding: the limited set of factorizable gravities can be attributed to the “straightjacket” imposed by the purely-adjoint color-kinematics duality with its unique color representation.
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