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We construct a non-relativistic limit of ten-dimensional N = 1 supergravity from the point of view of the symmetries, the action, and the equations of motion. This limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called ‘self-dual’ Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action exhibits three emerging symmetries: one local scale symmetry and two local conformal supersymmetries. Due to these emerging symmetries the Poisson equation for the Newton potential and two partner fermionic equations do not follow from a variation of the non-relativistic action but, instead, are obtained by a supersymmetry variation of the other equations of motion that do follow from a variation of the non-relativistic action. We shortly discuss the inclusion of the Yang-Mills sector that would lead to a non-relativistic heterotic supergravity action. [ABSTRACT FROM AUTHOR]

We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry. [ABSTRACT FROM AUTHOR]

We give a short overview of Newton-Cartan geometry and gravity including its matter couplings. We also present results on a new non-relativistic gravity model in three spacetime dimensions, called extended Bargmann gravity, and show that this model has matter couplings that differ from those of Newton-Cartan gravity. [ABSTRACT FROM AUTHOR]

We construct a N = 2 supersymmetric extension of Newton-Cartan gravity by gauging a N = 2 supersymmetric extension of the Bargmann algebra. Due to technical complications we restrict the construction to the three-dimensional case. We discuss the gauge-fixing of the resulting Newton-Cartan supergravity theory to a Galilean supergravity that contains the Newton potential. An unusual feature is that, in order to realize the supersymmetry on the Newton potential, we need to introduce a dual Newton potential as well. Together, Newton potential and dual potential, they form a holomorphic function of the two spatial coordinates. We briefly discuss the four-dimensional case. [ABSTRACT FROM AUTHOR]

We define an iterative procedure to obtain a non-abelian generalization of the BornInfeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. We have calculated all bosonic terms in the action up to terms quartic in the Yang-Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric trace-prescription. [ABSTRACT FROM AUTHOR]

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonic d=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphere S as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic space S, and can be rewritten as $$\mathop {\lim }\limits_{N \to \infty } su(N,N)$$ . As an application of our results, we formulate a new d=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms of S. [ABSTRACT FROM AUTHOR]

We define an iterative procedure to obtain a non-Abelian generalization of the Born-Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. In this paper we will present all bosonic terms in the action up to terms quartic in the Yang-Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric trace-prescription. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]