String Theory and String Newton-Cartan Geometry

Abstract

Nonrelativistic string theory is described by a sigma model with a relativistic worldsheet and a nonrelativistic target spacetime geometry, that is called string Newton-Cartan geometry. In this paper we obtain string Newton-Cartan geometry as a limit of the Riemannian geometry of General Relativity with a fluxless two-form field. We then apply the same limit to relativistic string theory in curved background fields and show that it leads to nonrelativistic string theory in a string Newton-Cartan geometry coupled to a Kalb-Ramond and dilaton field background. Finally, we use our limiting procedure to study the spacetime equations of motion and the T-duality transformations of nonrelativistic string theory. Our results reproduce the recent studies of beta-functions and T-duality of nonrelativistic string theory obtained from the microscopic worldsheet definition of nonrelativistic string theory.

arXiv comment41 pages

References in corpus (33)

• M Theory As A Matrix Model: A Conjecture
• Duality, Quotients, and Currents
• Why is the Matrix Model Correct?
• Non-Relativistic Closed String Theory
• Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory
• Non-Relativistic Superstrings: A New Soluble Sector of AdS_5xS^5
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• IIA/B, Wound and Wrapped
• S-Duality and Noncommutative Gauge Theory
• `Stringy' Newton-Cartan Gravity
• Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Nonrelativistic String Theory and T-Duality
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Compactification in the Lightlike Limit
• Non-relativistic strings and branes as non-linear realizations of Galilei groups
• Extended Galilean symmetries of non-relativistic strings
• Nonrelativistic String Theory in Background Fields
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• Newton-Cartan Gravity and Torsion
• An Action for Extended String Newton-Cartan Gravity
• 1+1 Dimensional NCOS and its U(N) Gauge Theory Dual
• Tachyons in the Galilean limit
• The Galilean Superstring
• Nonrelativistic String Theory Sigma Model and Its Canonical Formulation
• Probing tachyon kinks in Newton-Cartan background
• Non-Lorentzian M5-brane Theories from Holography
• Galilean free Lie algebras
• (m,n)-String and D1-Brane in Stringy Newton-Cartan Background
• Note About T-duality of Non-Relativistic String
• Renormalization properties of a Galilean Wess-Zumino model
• Hamiltonian For String in Newton-Cartan Background
• Stringy (Galilei) Newton-Hooke Chern-Simons Gravities

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• Non-Relativistic Gravity and its Coupling to Matter
• Aspects of Nonrelativistic Strings
• Review on Non-Relativistic Gravity
• 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
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Torsional Deformation of Nonrelativistic String Theory
• Dual D-Brane Actions in Nonrelativistic String Theory
• Nonrelativistic Open String and Yang-Mills Theory
• T-Duality in Nonrelativistic Open String Theory
• Non-relativistic duality and $T\bar{T}$ deformations
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Non-Riemannian isometries from double field theory
• Aspects of Non-Relativistic Quantum Field Theories
• Non-Riemannian gravity actions from double field theory
• 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
• Emergent Dipole Gauge Fields and Fractons
• The Non-Relativistic Geometric Trinity of Gravity
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• 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
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• The Panorama of Spin Matrix Theory
• Anisotropic Compactification of Nonrelativistic M-Theory
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Coset space actions for nonrelativistic strings
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Branched SL(2,Z) Duality
• Decoding the Spin-Matrix limit of strings on $Ad{S}_5\times S^5$
• Carroll Hawking effect
• Identifying Riemannian singularities with regular non-Riemannian geometry
• Nonrelativistic expansion of M2 branes and M theory backgrounds
• Null Dimensional Reduction of M2-Brane
• Light-Cone Gauge in Non-Relativistic AdS${}_5\times$S${}^5$ String Theory
• Non-relativistic string monodromies
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Non-Relativistic Holography from AdS${}_5$/CFT${}_4$
• Multispin magnons from Spin-Matrix strings on $Ad{S}_5\times S^5$
• Non-relativistic limit of gravity theories in the first order formalism
• Stringy Newton Gravity with $H$-flux
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• KLT Factorization of Winding String Amplitudes
• Stable and Unstable Dp-branes in p-brane Newton-Cartan Background
• Setting the connection free in the Galilei and Carroll expansions of gravity
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Non-Relativistic Supersymmetry on Curved Three-Manifolds
• Nonrelativistic strings on $R\times S^2$ and integrable systems
• D-Brane Actions in Non-Relativistic String Theory and T-Duality
• A perturbative approach to the non-relativistic string spectrum
• Nonrelativistic spinning strings
• Lagrangians for non-relativistic gravity
• Strings in Bimetric Spacetimes
• Traversable wormhole for string, but not for particle
• Gravitational Core of Double Field Theory: Lecture Notes
• Non-relativistic quantum strings from gauged WZW models
• Nonrelativistic expansion of type IIA NS5 brane
• Tensionless Tales: Vacua and Critical Dimensions
• Universal Box Operator: $\mathbf{O}(D,D)$-Symmetry and ${\alpha }^{\prime }$-Corrections
• On Twisted Spacetimes: a new class of Galilean cosmological models
• Nonrelativistic strings and the limits of $\mathcal{N}=2$ dualities
• Nonrelativistic limit of the bosonic string
• Holographic duals of $\mathcal{N}=1$ quivers in 5d and their nonrelativistic limits
• A Passion for Theoretical Physics: a special issue in memory of Peter G. O. Freund