Torsional string Newton-Cartan geometry for non-relativistic strings

Abstract

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 Inonu-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.

arXiv comment21+11 pages

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• Nonrelativistic expansion of M2 branes and M theory backgrounds
• Non-relativistic string monodromies
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• Non-relativistic quantum strings from gauged WZW models
• New Non-Relativistic String in AdS(5)xS(5)
• Canonical Analysis of New Non-Relativistic String Action and Uniform Light-Cone Gauge Formulation
• Nonrelativistic expansion of type IIA NS5 brane
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