Abstract
We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré∞, and we show that it contains among others an (A)dS quotient. We discuss a non-linear realisation of this infinite-dimensional algebra, and construct a particle action based on it. The latter yields a geodesic equation that includes (A)dS curvature corrections at every order.
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Gomis, J., Kleinschmidt, A., Roest, D. et al. A free Lie algebra approach to curvature corrections to flat space-time. J. High Energ. Phys. 2020, 68 (2020). https://doi.org/10.1007/JHEP09(2020)068
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DOI: https://doi.org/10.1007/JHEP09(2020)068