Abstract
We study gauge fields of arbitrary spin in de Sitter space. These include Yang-Mills fields and gravitons, as well as the higher-spin fields of Vasiliev theory. We focus on antipodally symmetric solutions to the field equations, i.e. ones that live on “elliptic” de Sitter space \( d{S}_4/{\mathrm{\mathbb{Z}}}_2 \). For free fields, we find spanning sets of such solutions, including boundary-to-bulk propagators. We find that free solutions on \( d{S}_4/{\mathrm{\mathbb{Z}}}_2 \) can only have one of the two types of boundary data at infinity, meaning that the boundary 2-point functions vanish. In Vasiliev theory, this property persists order by order in the interaction, i.e. the boundary n-point functions in \( d{S}_4/{\mathrm{\mathbb{Z}}}_2 \) all vanish. This implies that a higher-spin dS/CFT based on the Lorentzian \( d{S}_4/{\mathrm{\mathbb{Z}}}_2 \) action is empty. For more general interacting theories, such as ordinary gravity and Yang-Mills, we can use the free-field result to define a well-posed perturbative initial value problem in \( d{S}_4/{\mathrm{\mathbb{Z}}}_2 \).
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Neiman, Y. Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space. J. High Energ. Phys. 2014, 153 (2014). https://doi.org/10.1007/JHEP10(2014)153
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DOI: https://doi.org/10.1007/JHEP10(2014)153