# 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…

## 14 Citations

### The Weyl double copy from twistor space

- PhysicsJournal of High Energy Physics
- 2021

The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, and relates fields in spacetime directly. Where this procedure comes from, and how…

### Self-dual gravity and color/kinematics duality in AdS$_4$

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We show that self-dual gravity in Euclidean four-dimensional Anti-de Sitter space (AdS$_4$) can be described by a minimally coupled scalar field with a cubic interaction written in terms of a…

### Radiative phase space extensions at all orders in r for self-dual Yang-Mills and gravity

- MathematicsJournal of High Energy Physics
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Working in the self-dual sector for Yang-Mills and gravity, we show how to construct an extended phase space at null infinity, to all orders in the radial expansion. This formalises the symmetry…

### Lagrangians Manifesting Color-Kinematics Duality in the NMHV Sector of Yang-Mills

- Physics
- 2022

: Scattering amplitudes in Yang-Mills theory are known to exhibit kinematic structures which hint to an underlying kinematic algebra that is dual to the gauge group color algebra. This…

### BRST symmetry and the convolutional double copy

- Materials ScienceJournal of High Energy Physics
- 2022

Motivated by the results of Anastasiou et al., we consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories in more detail. We give a…

### Snowmass White Paper: the Double Copy and its Applications

- Physics
- 2022

: The double copy is, in essence, a map between scattering amplitudes in a broad variety of familiar ﬁeld and string theories. In addition to the mathematically rich intrinsic structure, it underlies…

### Off-shell color-kinematics duality for Chern-Simons

- PhysicsJournal of High Energy Physics
- 2022

Many gauge theories possess a hidden duality between color and kinematics in their on-shell scattering amplitudes. An open problem is to formulate an off-shell realization of the duality, thus…

### NS-NS spacetimes from amplitudes

- PhysicsJournal of High Energy Physics
- 2022

Recent work has shown how on-shell three-point amplitudes in gauge theory and gravity, representing the coupling to massive particles, correspond in the classical limit to the curvature spinors of…

### Alternative formulations of the twistor double copy

- MathematicsJournal of High Energy Physics
- 2022

The classical double copy relating exact solutions of biadjoint scalar, gauge and gravity theories continues to receive widespread attention. Recently, a derivation of the exact classical double copy…

### Double copy for Lagrangians at trilinear order

- PhysicsJournal of High Energy Physics
- 2022

We present a novel double-copy prescription for gauge fields at the Lagrangian level and apply it to the original double copy, couplings to matter and the soft theorem. The Yang-Mills Lagrangian in…

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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…