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.

21+11 pages

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• Revisiting non-relativistic limits
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• Dual D-Brane Actions in Nonrelativistic String Theory
• Unification of Decoupling Limits in String and M-theory
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Aspects of Non-Relativistic Quantum Field Theories
• Worldsheet Formalism for Decoupling Limits in String Theory
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• Emergent Dipole Gauge Fields and Fractons
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Generalized Newton-Cartan Geometries for Particles and Strings
• Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors
• KLT Factorization of Nonrelativistic String Amplitudes
• Anisotropic Compactification of Nonrelativistic M-Theory
• The Panorama of Spin Matrix Theory
• Branched SL(2,Z) Duality
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Coset space actions for nonrelativistic strings
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• Nonrelativistic expansion of M2 branes and M theory backgrounds
• Non-relativistic string monodromies
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• Non-relativistic quantum strings from gauged WZW models
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