Torsional Newton Cartan gravity from non-relativistic strings

Abstract

We study propagation of closed bosonic strings in torsional Newton-Cartan geometry based on a recently proposed Polyakov type action derived by dimensional reduction of the ordinary bosonic string along a null direction. We generalize the Polyakov action proposal to include matter, i.e. the 2-form and the 1-form that originates from the Kalb-Ramond field and the dilaton. We determine the conditions for Weyl invariance which we express as the beta-function equations on the worldsheet, in analogy with the usual case of strings propagating on a pseudo-Riemannian manifold. The critical dimension of the TNC space-time turns out to be 25. We find that Newton's law of gravitation follows from the requirement of quantum Weyl invariance in the absence of torsion. Presence of the 1-form requires torsion to be non vanishing. Torsion has interesting consequences, in particular it yields a mass term and an advection term in the generalized Newton's law. U(1) mass invariance of the theory is an important ingredient in deriving the beta functions.

arXiv commentSummary of results added. Reorganization and generalization of results. Typos fixed

References in corpus (23)

• Non-Relativistic Closed String Theory
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Newtonian Gravity and the Bargmann Algebra
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Action Principle for Newtonian Gravity
• `Stringy' Newton-Cartan Gravity
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• On the coupling of Galilean-invariant field theories to curved spacetime
• Nonrelativistic String Theory and T-Duality
• Non-Relativistic Gravity and its Coupling to Matter
• Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity
• Nonrelativistic String Theory in Background Fields
• A new formulation of non-relativistic diffeomorphism invariance
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• Newton-Cartan Gravity and Torsion
• A worldsheet supersymmetric Newton-Cartan string
• An Action for Extended String Newton-Cartan Gravity
• Torsional Newton-Cartan Geometry from the Noether Procedure
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Torsional Newton-Cartan geometry from Galilean gauge theory
• Nonrelativistic pulsating strings
• Semiclassical dynamics for torsional Newton-Cartan strings
• Nonrelativistic giant magnons from Newton Cartan strings

Cited by in corpus (39)

• Aspects of Nonrelativistic Strings
• Torsional string Newton-Cartan geometry for non-relativistic strings
• A Non-Relativistic Limit of NS-NS Gravity
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• Torsional Deformation of Nonrelativistic String Theory
• Dual D-Brane Actions in Nonrelativistic String Theory
• Nonrelativistic Open String and Yang-Mills Theory
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Non-Riemannian isometries from double field theory
• Non-Riemannian gravity actions from double field theory
• Geometrizing non-relativistic bilinear deformations
• Worldsheet Formalism for Decoupling Limits in String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Super-Carrollian and Super-Galilean Field Theories
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Generalized Newton-Cartan Geometries for Particles and Strings
• KLT Factorization of Nonrelativistic String Amplitudes
• The Panorama of Spin Matrix Theory
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Branched SL(2,Z) Duality
• Coset space actions for nonrelativistic strings
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Nonrelativistic expansion of M2 branes and M theory backgrounds
• Light-Cone Gauge in Non-Relativistic AdS${}_5\times$S${}^5$ String Theory
• Non-Relativistic Holography from AdS${}_5$/CFT${}_4$
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Setting the connection free in the Galilei and Carroll expansions of gravity
• KLT Factorization of Winding String Amplitudes
• A perturbative approach to the non-relativistic string spectrum
• Nonrelativistic expansion of type IIA NS5 brane
• Tensionless Tales: Vacua and Critical Dimensions
• Holographic duals of $\mathcal{N}=1$ quivers in 5d and their nonrelativistic limits