Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions

Abstract

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 $\times$ 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 $\times$ gauge' convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

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Cited by in corpus (12)

• Off-Shell Color-Kinematics Duality for Chern-Simons
• Asymptotic Weyl Double Copy
• Alternative formulations of the twistor double copy
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Double copy for Lagrangians at trilinear order
• BRST Symmetry and the Convolutional Double Copy
• The double copy: from optics to quantum gravity
• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• NS-NS Spacetimes from Amplitudes
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group