The kinematic algebra from the self-dual sector

By R. Monteiro, D. O’Connell. 2011

285 citations recorded by the source corpus.

We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b3db451258fe86cf2737ace5e3401f5c4227b628

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Citations in the corpus

The double copy: Bremsstrahlung and accelerating black holes (2016, background): “The validity of the BCJ double copy and the existence of colour-dual numerators has been proven at tree-level [5–13] (where it is equivalent to the KLT relations [1]).”
Perturbative spacetimes from Yang-Mills theory (2016, methodology): “ty, and hints at an intriguing correspondence between colour and kinematic degrees of freedom that is still not fully understood, although progress has been made in the self-dual sector of the theory [4]. More generally, the eld-theory limit of superstring theory has been very fruitful for understan”
The classical double copy for Taub–NUT spacetime (2015, background): “[20,54] where, in the latter, the Yang-Mills action can be made manifestly cubic [55], and a full interpretation of BCJ duality obtained.”
Type D spacetimes and the Weyl double copy (2018, unknown): “interesting example that it applies to is the Kerr-Taub-NUT family of solutions [49]. The self-dual sector of gauge theory and gravity is another natural setting to study the double copy, as found in [50] at the perturbative level. Very recently, the Eguchi-Hanson metric was studied in this context ”
Black holes and the double copy (2014, methodology): “[49] can be expressed using a momentum-space generalisation of Kerr-Schild coordinates.”
One-loop amplitudes on the Riemann sphere (2015, background): “ng the reference spinor ji, X i;j = [^i^j] = X j;i : (3.29) The direct \square" relation between the rules in gauge theory and in gravity makes the BCJ double copy manifest for these amplitudes [62]. Using the diagrammatic rules above, we can write the (shifted) integrand for the single-trace c”
The Kerr-Schild double copy in curved spacetime (2017, methodology): “ahlung of photon and graviton radiation, thus more tightly establishing the link between the classical and amplitude double copies. Reference [70] went beyond the simple Kerr-Schild form used in ref. [10], in considering the TaubNUT solution. This has a double Kerr-Schild form, yet nevertheless can ”
TASI Lectures on Scattering Amplitudes (2017, background): “des are built from separately Lorentz invariant numerators. Recent years have seen incremental progress towards an action-level understanding of these structures. For instance, Monteiro and O’Connell [124] beautifully demonstrated how the self-dual sector of YM theory squares into self-dual gravity.”