Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

We show that our previous work on Galilei and Carroll gravity, apt for particles, can be generalized to Galilei and Carroll gravity theories adapted to p-branes (p = 0, 1, 2, ⋯). Within this wider brane perspective, we make use of a formal map, given in the literature, between the corresponding p-brane Carroll and Galilei algebras where the index describing the directions longitudinal (transverse) to the Galilei brane is interchanged with the index covering the directions transverse (longitudinal) to the Carroll brane with the understanding that the time coordinate is always among the longitudinal directions. This leads among other things in 3D to a map between Galilei particles and Carroll strings and in 4D to a similar map between Galilei strings and Carroll strings. We show that this formal map extends to the corresponding Lie algebra expansion of the Poincaré algebra and, therefore, to several extensions of the Carroll and Galilei algebras including central extensions. We use this formal map to construct several new examples of Carroll gravity actions. Furthermore, we discuss the symmetry between Carroll and Galilei at the level of the p-brane sigma model action and apply this formal symmetry to give several examples of 3D and 4D particles and strings in a curved Carroll background.

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“…The case p = 0, q = 1 corresponds to the usual Wigner-Inönü contraction 4. This subsection has some overlap with the recent paper[24].…”

mentioning

confidence: 89%

“…In the case of AdS this relation between Galilean and Carroll expansions was studied in[24] 2. Our nomenclature of the different algebras and gravity theories occurring in this work is explained in appendix A.…”

mentioning

confidence: 99%

Carroll versus Galilei from a brane perspective

Bergshoeff

Izquierdo

Romanò

2020

J. High Energ. Phys.

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“…The NR version of the Maxwell CS gravity theory has only been presented recently [71] (see also [72], where the related algebra has been recovered through Lie algebra expansion).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Maxwellian extended Bargmann supergravity

Concha

Ravera

Rodríguez

2020

J. High Energ. Phys.

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We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the nonrelativistic limits of the minimal and the N = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

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“…The first, somewhat trivial, example of such a family of hypersurfaces we consider is 13) so that the hypersurfaces are labelled only by the coordinate x a (0) and the values of the x a (m) with m > 0 can take any value and are unconstrained. Note that z a has dimension of length according to dimensions of the x a (m) discussed below (3.1).…”

Section: (M)mentioning

confidence: 99%

“…The Galilei algebra appears as a simplest quotient of this algebra, while taking bigger quotients one obtains the non-relativistic algebras studied in [6-10, 12, 13]. When including corrections at all orders, this becomes an infinite-dimensional algebra [7,8,13,14]. The Poincaré algebra arises as a finite-dimensional quotient of this.…”

Section: Introductionmentioning

confidence: 99%

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

Gomis

Kleinschmidt

Roest

et al. 2020

J. High Energ. Phys.

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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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Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

Cited by 58 publications

References 85 publications

Carroll versus Galilei from a brane perspective

Carroll versus Galilei from a brane perspective

Three-dimensional Maxwellian extended Bargmann supergravity

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

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