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.
Highlights
Applied to the notion of ‘gravity = gauge × gauge’
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
The gauge symmetry BRST transformations generate via the convolution the diffeomorphism BRST transformations of the graviton, to linear order
Summary
Ought to correspond to the universal Neveu-Schwarz sector of the α → 0 limit of closed string theories,. Aside from the metric g and cosmological constant Λ, we have the dilaton φ and the Kalb-Ramond (KR) 2-form B with field strength H = dB. This is sometimes referred to as N = 0 supergravity, for short. For a given gauge-fixing condition, the linearised QYM-invariant BRST action can be written. The Fierz-Pauli BRST complex consists of the ghost number gh = 0 gauge potential h, the 1-form diffeomorphism gh = 1 ghost ξ, and its accompanying 1-form trivial pair of the gh = 0 Nakanishi-Lautrup auxiliary field π and gh = −1 diffeomorphism antighost ξ.
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