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In the following comment and references, it is mentioned that gravity can be understood as yang mills squared. What is the Lagrangian of a Yang Mills squared theory? Can anyone provide a quick primer?

In this comment:

Why are string theorist so indifferent to the gauge structure of gravity?

Then in these references:

https://arxiv.org/abs/1602.08267

https://www.youtube.com/watch?v=JTUQw2wxck8

Qmechanic
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Anon21
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1 Answers1

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  1. The statement $$ \text{(super) gravity} = [\text{(super) Yang-Mills]}^2 $$ is the punch line of the Bern-Carrasco-Johansson (BCJ) colour-kinematic duality conjecture that the perturbative on-shell scattering amplitudes for (super) gravity are the double-copy of gluon scattering amplitudes in (super) Yang-Mills theory.

  2. Refs. 1-2 are some recent work on implementing manifest BCJ colour-kinematic duality at the level of the off-shell action/Lagrangian, cf. OP's title question.

References:

  1. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann & M. Wolf, BRST-Lagrangian Double Copy of Yang-Mills Theory, arXiv:2007.13803.

  2. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann & M. Wolf, Double Copy from Homotopy Algebras, arXiv:2102.11390.

Qmechanic
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