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

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2006.11102.pdf

(Preprint), 290KB

Gomis2020_Article_AFreeLieAlgebraApproachToCurva.pdf

(Publisher version), 393KB

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##### Citation

Gomis, J., Kleinschmidt, A., Roest, D., & Salgado-Rebolledo, P. (2020). A free
Lie algebra approach to curvature corrections to flat space-time.* Journal of High Energy Physics,*
*2020*(9): 68. doi:10.1007/JHEP09(2020)068.

Cite as: https://hdl.handle.net/21.11116/0000-0006-99E6-A

##### 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.

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.