Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
High Energy Physics - Theory
2021-07-07 v2 Mathematical Physics
math.MP
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 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 product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.
Cite
@article{arxiv.2104.01135,
title = {Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions},
author = {L. Borsten and I. Jubb and V. Makwana and S. Nagy},
journal= {arXiv preprint arXiv:2104.01135},
year = {2021}
}