Gauge × 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 × gauge'. In particular, it is shown that the linear BecchiRouetStoraTyutin (BRST) gauge transformations of two YangMills 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 June 2021
 DOI:
 10.1007/JHEP06(2021)117
 arXiv:
 arXiv:2104.01135
 Bibcode:
 2021JHEP...06..117B
 Keywords:

 BRST Quantization;
 Gauge Symmetry;
 Gaugegravity correspondence;
 SpaceTime Symmetries;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 doi:10.1007/JHEP06(2021)117