Nonrelativistic String Theory and T-Duality

Abstract

Nonrelativistic string theory in flat spacetime is described by a two-dimensional quantum field theory with a nonrelativistic global symmetry acting on the worldsheet fields. Nonrelativistic string theory is unitary, ultraviolet complete and has a string spectrum and spacetime S-matrix enjoying nonrelativistic symmetry. The worldsheet theory of nonrelativistic string theory is coupled to a curved spacetime background and to a Kalb-Ramond two-form and dilaton field. The appropriate spacetime geometry for nonrelativistic string theory is dubbed string Newton-Cartan geometry, which is distinct from Riemannian geometry. This defines the sigma model of nonrelativistic string theory describing strings propagating and interacting in curved background fields. We also implement T-duality transformations in the path integral of this sigma model and uncover the spacetime interpretation of T-duality. We show that T-duality along the longitudinal direction of the string Newton-Cartan geometry describes relativistic string theory on a Lorentzian geometry with a compact lightlike isometry, which is otherwise only defined by a subtle infinite boost limit. This relation provides a first principles definition of string theory in the discrete light cone quantization (DLCQ) in an arbitrary background, a quantization that appears in nonperturbative approaches to quantum field theory and string/M-theory, such as in Matrix theory. T-duality along a transverse direction of the string Newton-Cartan geometry equates nonrelativistic string theory in two distinct, T-dual backgrounds.

26 pages; v2: minor clarifications, a reference added; v3: clarifications, references added, fixed typos

References in corpus (7)

• Galilean Conformal Algebras and AdS/CFT
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Nonrelativistic String Theory and T-Duality
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Extended Galilean symmetries of non-relativistic strings
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• The Galilean Superstring

Cited by in corpus (93)

• Action Principle for Newtonian Gravity
• Nonrelativistic String Theory and T-Duality
• Non-Relativistic Gravity and its Coupling to Matter
• Carroll Expansion of General Relativity
• String Theory and String Newton-Cartan Geometry
• Relating non-relativistic string theories
• Aspects of Nonrelativistic Strings
• Nonrelativistic String Theory in Background Fields
• Carrollian and celestial spaces at infinity
• Torsional string Newton-Cartan geometry for non-relativistic strings
• A Non-Relativistic Limit of NS-NS Gravity
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Lie Algebra Expansions and Actions for Non-Relativistic Gravity
• Torsional Newton Cartan gravity from non-relativistic strings
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• A worldsheet supersymmetric Newton-Cartan string
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• An Action for Extended String Newton-Cartan Gravity
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Torsional Deformation of Nonrelativistic String Theory
• Remarks on the non-Riemannian sector in Double Field Theory
• Dual D-Brane Actions in Nonrelativistic String Theory
• Nonrelativistic Open String and Yang-Mills Theory
• Unification of Decoupling Limits in String and M-theory
• T-Duality in Nonrelativistic Open String Theory
• Non-Riemannian geometry of M-theory
• Non-relativistic duality and $T\bar{T}$ deformations
• Oddity in nonrelativistic, strong gravity
• Newton-Cartan Submanifolds and Fluid Membranes
• 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
• Galilean first-order formulation for the non-relativistic expansion of general relativity
• Galilean free Lie algebras
• Geometrizing non-relativistic bilinear deformations
• Worldsheet Formalism for Decoupling Limits in String Theory
• Carroll versus Galilei from a Brane Perspective
• (m,n)-String and D1-Brane in Stringy Newton-Cartan Background
• Non-Relativistic M2-Brane
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Note About T-duality of Non-Relativistic String
• Matrix Theory Reloaded: A BPS Road to Holography
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Nonrelativistic pulsating strings
• p-brane Newton--Cartan Geometry
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors
• Generalized Newton-Cartan Geometries for Particles and Strings
• Nonrelativistic Corners of $\mathcal{N}=4$ Supersymmetric Yang--Mills Theory
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Non-Relativistic D-brane from T-duality Along Null Direction
• KLT Factorization of Nonrelativistic String Amplitudes
• Anisotropic Compactification of Nonrelativistic M-Theory
• The Panorama of Spin Matrix Theory
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Branched SL(2,Z) Duality
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Coset space actions for nonrelativistic strings
• Stringy (Galilei) Newton-Hooke Chern-Simons Gravities
• Supersymmetric Galilean Electrodynamics
• 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${}_4$
• Nonrelativistic giant magnons from Newton Cartan strings
• Covariant Poisson's equation in torsional Newton-Cartan gravity
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?
• KLT Factorization of Winding String Amplitudes
• How to Build a Black Hole out of Instantons
• 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
• Fractonic self-duality and covariant magnetic fractons
• Renormalization of Supersymmetric Lifshitz Sigma Models
• A perturbative approach to the non-relativistic string spectrum
• D-Brane Actions in Non-Relativistic String Theory and T-Duality
• Lagrangians for non-relativistic gravity
• Newton-Cartan $D0$ branes from $D1$ branes and integrability
• String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds
• Gravitational Core of Double Field Theory: Lecture Notes
• Non-relativistic quantum strings from gauged WZW models
• A new approach for nonrelativistic bosonic string in flat space time
• Geometry of Nonrelativistic string
• Nonrelativistic expansion of type IIA NS5 brane
• Nonrelativistic strings and the limits of $\mathcal{N}=2$ dualities
• Holographic duals of $\mathcal{N}=1$ quivers in 5d and their nonrelativistic limits