Erratum to: Oddity in nonrelativistic, strong gravity

We discuss a general methodology to provide rigid, off-shell matter multiplets and actions for recently constructed non-relativistic superalgebras. The technique is based on the Lie algebra expansion, which, in the context of supersymmetry, has so far been used to obtain non-relativistic on-shell supergravity models. We first explain how the Lie algebra expansion can be implemented to generate off-shell rigid multiplets on a flat background by developing an auxiliary framework where only the lowest order behavior of the spatial and temporal vielbein is relevant. We then provide explicit examples for the field content, the transformation rules as well as action principles for certain multiplets in three and four dimensions.

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Lie algebra expansions, non-relativistic matter multiplets and actions

Kasikci

Ozkan

2022

J. High Energ. Phys.

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Non-relativistic three-dimensional supergravity theories and semigroup expansion method

Concha

Ipinza

Ravera

et al. 2021

J. High Energ. Phys.

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In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.

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Torsional string Newton-Cartan geometry for non-relativistic strings

Bidussi

Harmark

Hartong

et al. 2022

J. High Energ. Phys.

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We revisit the formulation of non-relativistic (NR) string theory and its target space geometry. We obtain a new formulation in which the geometry contains a two-form field that couples to the tension current and that transforms under string Galilei boosts. This parallels the Newton-Cartan one-form that couples to the mass current of a non-relativistic point particle. We show how this formulation of the NR string arises both from an infinite speed of light limit and a null reduction of the relativistic closed bosonic string. In both cases, the two-form originates from a combination of metric quantities and the Kalb-Ramond field. The target space geometry of the NR string is seen to arise from the gauging of a new algebra that is obtained by an İnönü-Wigner contraction of the Poincaré algebra extended by the symmetries of the Kalb-Ramond field. In this new formulation, there are no superfluous target space fields that can be removed by fixing a Stückelberg symmetry. Classically, there are no foliation/torsion constraints imposed on the target space geometry.

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Erratum to: Oddity in nonrelativistic, strong gravity

Abstract: In the original version of this article, the last name of the second author missed its last letter.

Cited by 14 publications

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Lie algebra expansions, non-relativistic matter multiplets and actions

Lie algebra expansions, non-relativistic matter multiplets and actions

Non-relativistic three-dimensional supergravity theories and semigroup expansion method

Torsional string Newton-Cartan geometry for non-relativistic strings

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