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

par Gomis, Joaquim;Kleinschmidt, Axel ;Roest, Diederik;Salgado-Rebolledo, Patricio
Référence The journal of high energy physics (Online), 2020, 9, 68
Publication Publié, 2020-09

Article révisé par les pairs

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Résumé :

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.