Torsional Newton-Cartan Geometry from the Noether Procedure

Abstract

We apply the Noether procedure for gauging space-time symmetries to theories with Galilean symmetries, analyzing both massless and massive (Bargmann) realizations. It is shown that at the linearized level the Noether procedure gives rise to (linearized) torsional Newton-Cartan geometry. In the case of Bargmann theories the Newton-Cartan form $M_{\mu }$ couples to the conserved mass current. We show that even in the case of theories with massless Galilean symmetries it is necessary to introduce the form $M_{\mu }$ and that it couples to a topological current. Further, we show that the Noether procedure naturally gives rise to a distinguished affine (Christoffel type) connection that is linear in $M_{\mu }$ and torsionful. As an application of these techniques we study the coupling of Galilean electrodynamics to TNC geometry at the linearized level.

arXiv comment31 pages; v2 references added

References in corpus (34)

• Gravity Duals of Lifshitz-like Fixed Points
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Membranes at Quantum Criticality
• A healthy extension of Horava gravity
• Non-relativistic holography
• General Covariance in Quantum Gravity at a Lifshitz Point
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Newtonian Gravity and the Bargmann Algebra
• Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
• Spacetime Symmetries of the Quantum Hall Effect
• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Lifshitz Space-Times for Schroedinger Holography
• Supercurrents and Brane Currents in Diverse Dimensions
• Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
• On the coupling of Galilean-invariant field theories to curved spacetime
• Warped Conformal Field Theory as Lower Spin Gravity
• Newton-Cartan Geometry and the Quantum Hall Effect
• Three-Dimensional Extended Bargmann Supergravity
• Newton-Cartan Supergravity
• Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
• Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
• Newton-Cartan (super)gravity as a non-relativistic limit
• Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
• General coordinate invariance in quantum many-body systems
• Non-relativistic fields from arbitrary contracting backgrounds
• Torsional Newton-Cartan geometry from Galilean gauge theory
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Conformal and projective symmetries in Newtonian cosmology
• Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry
• Newton-Cartan supergravity with torsion and Schrödinger supergravity

Cited by in corpus (25)

• Action Principle for Newtonian Gravity
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Perfect Fluids
• Non-Relativistic Gravity and its Coupling to Matter
• Review on Non-Relativistic Gravity
• Non-Boost Invariant Fluid Dynamics
• Non-Relativistic Ten-Dimensional Minimal Supergravity
• Torsional Newton Cartan gravity from non-relativistic strings
• Newton-Cartan Gravity and Torsion
• Oddity in nonrelativistic, strong gravity
• Newton-Cartan Submanifolds and Fluid Membranes
• Geometrizing non-relativistic bilinear deformations
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• Effective field theory for non-relativistic hydrodynamics
• Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors
• Three-dimensional non-relativistic supergravity and torsion
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Hydrodynamics of thermal active matter
• Enstrophy without boost symmetry
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• Symmetries and Couplings of Non-Relativistic Electrodynamics
• Canonical Formalism of Non-Relativistic Theories Coupled to Newton-Cartan Gravity
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter