Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

@article{Borsten2021GaugeG,
  title={Gauge × gauge = gravity on homogeneous spaces using tensor convolutions},
  author={Leron Borsten and Ian Jubb and V. Makwana and Silvia Nagy},
  journal={Journal of High Energy Physics},
  year={2021},
  volume={2021}
}
A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution… 
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14 Citations

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93 References

Riemannian Geometry

THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss's…

Ehlers transformations as EM duality in the double copy

Given a solution to 4D Einstein gravity with an isometry direction, it is known that the equations of motion are identical to those of a 3D $\sigma$-model with target space geometry $SU(1,1)/U(1)$.…

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM

A bstractThe tree-level S-matrix of Einstein’s theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering…

Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes.

It is shown that one can start from generic gauge-theory integrands, where the duality is not manifest, and apply a modified double-copy procedure to obtain gravity integrand that include contact terms generated by violations of dual Jacobi identities.

The convolutional double copy: a case study with a point

The double copy relates scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, and a number of approaches have been developed for doing so. One of…

Yang-Mills origin of gravitational symmetries.

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry are derived.

Type D spacetimes and the Weyl double copy

We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important…

The Kerr-Schild double copy in curved spacetime

A bstractThe double copy is a much-studied relationship between scattering amplitudes in gauge and gravity theories, that has subsequently been extended to classical field solutions. In nearly all…

Gravity as Gauge Theory Squared: A Ghost Story.

The Becchi-Rouet-Stora-Tyutin (BRST) transformations and equations of motion of a gravity-two-form-dilaton system are derived from the product of two Yang-Mills theories in a BRST covariant form, to…

Gauge × gauge on spheres

We introduce a convolution on a 2-sphere and use it to show that the linearised Becchi-Rouet-Stora-Tyutin transformations and gauge fixing conditions of Einstein-Hilbert gravity coupled to a two-form…
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