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arXiv · 2006.11102

A free Lie algebra approach to curvature corrections to flat space-time

Joaquim Gomis·Axel Kleinschmidt·Diederik Roest·Patricio Salgado-Rebolledo
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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 Poincar\'e 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 Poincar\'e${}_\infty$, 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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Joaquim Gomis, Axel Kleinschmidt, Diederik Roest, Patricio Salgado-Rebolledo. 2020-06-19. A free Lie algebra approach to curvature corrections to flat space-time. https://doi.org/10.1007/jhep09(2020)068

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