Extended Galilean symmetries of non-relativistic strings

Abstract

We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.

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References in corpus (29)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Galilean Conformal Algebras and AdS/CFT
• Non-Relativistic Closed String Theory
• Non-Relativistic Superstrings: A New Soluble Sector of AdS_5xS^5
• IIA/B, Wound and Wrapped
• Tensionless Strings and Galilean Conformal Algebra
• Local scale invariance and strongly anisotropic equilibrium critical systems
• Galileons as Wess-Zumino Terms
• Newton-Cartan Geometry and the Quantum Hall Effect
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Non-relativistic strings and branes as non-linear realizations of Galilei groups
• Galilean Isometries
• Non-Relativistic Superbranes
• Non-relativistic holography from Horava gravity
• Comments on Galilean conformal field theories and their geometric realization
• Scalar Field Theories with Polynomial Shift Symmetries
• Galilean Conformal Electrodynamics
• Affine Extension of Galilean Conformal Algebra in 2+1 Dimensions
• The Galilean Superstring
• A Membrane Action for OM Theory
• Galilean Yang-Mills Theory
• Rotating Solutions of Non-relativistic String Theory
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Surprises with Nonrelativistic Naturalness
• Symmetries and Couplings of Non-Relativistic Electrodynamics

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• Aspects of Nonrelativistic Strings
• Nonrelativistic String Theory in Background Fields
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Non-Relativistic Maxwell Chern-Simons Gravity
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• An Action for Extended String Newton-Cartan Gravity
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Confined dynamical systems with Carroll or Galilei symmetries
• Torsional Deformation of Nonrelativistic String Theory
• Nonrelativistic Open String and Yang-Mills Theory
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• Nonrelativistic Approximations of Closed Bosonic String Theory
• Nonrelativistic String Theory Sigma Model and Its Canonical Formulation
• The Galilean Superstring
• Tachyons in the Galilean limit
• Probing tachyon kinks in Newton-Cartan background
• Non-Riemannian isometries from double field theory
• Worldsheet Formalism for Decoupling Limits in String Theory
• Galilean free Lie algebras
• VSUSY models with Carroll or Galilei invariance
• Carroll versus Galilei from a Brane Perspective
• Symmetries of post-Galilean expansions
• Matrix Theory Reloaded: A BPS Road to Holography
• Nonrelativistic pulsating strings
• Semiclassical dynamics for torsional Newton-Cartan strings
• Note About Hamiltonian Formalism for Newton-Cartan String and p-Brane
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Coset space actions for nonrelativistic strings
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Extending the non-relativistic string AdS coset
• Stringy (Galilei) Newton-Hooke Chern-Simons Gravities
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Non-relativistic $k$-contractions of the Coadjoint Poincaré algebra
• Lax pairs for string Newton Cartan geometry
• Canonical Analysis of Non-Relativistic Particle and Superparticle
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Non-Relativistic Holography from AdS${}_5$/CFT${}_4$
• Hamiltonian Analysis of Non-Relativistic Non-BPS Dp-brane
• Remark About Non-Relativistic p-Brane
• Carroll Limit of Non-BPS Dp-Brane
• Contractions of the Maxwell algebra
• Note About Integrability of Non-Relativistic String
• Strings in Bimetric Spacetimes
• A pedagogical review of gravity as a gauge theory
• Non-relativistic quantum strings from gauged WZW models
• A new approach for nonrelativistic bosonic string in flat space time
• Space-time Schrödinger symmetries of a post-Galilean particle
• A non-lorentzian primer