V. Makwana | Searcharxiv

arXiv2021

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

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.

hep-th↗

arXiv2019

Gauge $\times$ 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 and a scalar field, follow from the product of two Yang-Mills theories. This provides an example of the convolutive product of gauge theories on a non-trivial background. By introducing a time direction the product is shown to extend to the $D=1+2$ Einstein-static universe.

hep-th↗