A pure-connection derivation yields Plebanski's second heavenly equation on flat and constant-curvature backgrounds, packaged in a compact covariant form with a new interpretation of the self-dual Yang-Mills kinematic algebra.
One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity
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abstract
We present an ansatz for all one-loop amplitudes in pure Einstein gravity for which the n external gravitons have the same outgoing helicity. These loop amplitudes, which are rational functions of the momenta, also arise in the quantization of self-dual gravity in four-dimensional Minkowski space. Our ansatz agrees with explicit computations via D-dimensional unitarity cuts for n less than or equal to 6. It also has the expected analytic behavior, for all n, as a graviton becomes soft, and as two momenta become collinear. The gravity results are closely related to analogous amplitudes in (self-dual) Yang-Mills theory.
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Pure connection formalism and Plebanski's second heavenly equation
A pure-connection derivation yields Plebanski's second heavenly equation on flat and constant-curvature backgrounds, packaged in a compact covariant form with a new interpretation of the self-dual Yang-Mills kinematic algebra.