Three-dimensional higher-order Schrödinger algebras and Lie algebra expansions
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In this article, a higher-order Schrodinger algebra was constructed for higher order non-relativistic algebras, which can accommodate three discrete Newtonian parameters.Abstract:
We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schrodinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the extended Schrodinger algebra and provide a new higher-order Schrodinger algebra. The structure of this new algebra leads to a discussion on the uniqueness of the higher-order non-relativistic algebras. Especially, we show that the recent d-dimensional symmetry algebra of an action principle for Newtonian gravity is not uniquely defined but can accommodate three discrete parameters. For a particular choice of these parameters, the Bargmann algebra becomes a subalgebra of that extended algebra which allows one to introduce a mass current in a Bargmann-invariant sense to the extended theory.read more
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Generalized maxwellian exotic bargmann gravity theory in three spacetime dimensions
TL;DR: In this article, a generalization of the so-called Maxwellian extended Bargmann algebra by considering a non-relativistic limit to a generalized Maxwell algebra defined in three spacetime dimensions is presented.
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Non-relativistic three-dimensional supergravity theories and semigroup expansion method
TL;DR: In this article, the authors apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions.
Journal ArticleDOI
Lie algebra expansion and integrability in superstring Sigma-models
TL;DR: In this article, the authors apply the method of Lie algebra expansion to superstring σ-models with a ℤ4 coset target space, and reproduce and extend in a systematic way actions of some known string regimes (flat space, BMN and non-relativistic in AdS5×S5).
Journal ArticleDOI
Three-dimensional non-relativistic extended supergravity with cosmological constant
TL;DR: In this article, two non-relativistic superalgebras which correspond to supersymmetric extensions of the enlarged extended Bargmann algebra have been constructed, which allow to accommodate a cosmological constant.
Journal ArticleDOI
Three-dimensional Maxwellian Extended Newtonian gravity and flat limit.
TL;DR: In this article, a non-relativistic limit of a particular $U(1)$-enlargement of an enhanced version of the Chern-Simons gravity was obtained as the limit of an enlarged symmetry, which was obtained by applying the semigroup expansion method to the Nappi-Witten algebra.
References
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Action Principle for Newtonian Gravity
TL;DR: In this article, the authors derive an action whose equations of motion contain the Poisson equation of Newtonian gravity, and derive a new notion of Newton-Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann algebra.
Journal ArticleDOI
Three-Dimensional Extended Bargmann Supergravity.
Eric Bergshoeff,Jan Rosseel +1 more
TL;DR: It is shown that three-dimensional general relativity, augmented with two vector fields, allows for a nonrelativistic limit, different from the standard limit leading to Newtonian gravity, that results in a well-defined action which is of the Chern-Simons type.
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