Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry

Abstract

We discuss a realization of the nonrelativistic conformal group (the Schroedinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field equations. We discuss various issues related to nonrelativistic holography. In particular, we argue that free fermions and fermions at unitarity correspond to the same bulk theory with different choices for the near-boundary asymptotics corresponding to the source and the expectation value of one operator. We describe an extended version of nonrelativistic general coordinate invariance which is realized holographically.

arXiv comment14 pages; v2: typos fixed, published version

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• Holographic Renormalization for Fermions in Real Time
• Holographic thermalization from non relativistic branes
• Crystalline geometries from fermionic vortex lattice with hyperscaling violation
• Holographic charge diffusion in non relativistic branes
• Holographic Thermodynamics and Transport of Flavor Fields
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Solitonic Phase Transitions of Galilean Black Holes
• Conformal bridge in a cosmic string background
• Yang-Baxter Deformations of the $Ad{S}_5\times T^{1,1}$ Superstring and their Backgrounds
• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Teleparallel formalism of galilean gravity
• Asymptotically Schrödinger Space-Times
• String Backgrounds of the Yang-Baxter Deformed $Ad{S}_4\times {\mathbb{CP}}^3$ Superstring
• A Holographic model for Non-Relativistic Superconductor
• Spatial Anisotropy in Nonrelativistic Holography
• Deep Inelastic Scattering on an Extremal RN-AdS Black Hole II: Holographic Fermi Surface
• Non-relativistic transport from frame-indifferent kinetic theory
• Galilean Conformal Algebra in Semi-Infinite Space
• Supersymmetric Carroll Galileons in Three Dimensions
• Aging Logarithmic Galilean Field Theories
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Perfect fluid dynamics with conformal Newton-Hooke symmetries
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Revisiting Wilson loops for nonrelativistic backgrounds
• Marginal Deformations of Non-Relativistic Field Theories
• Stationary Lifshitz Black Hole of New Massive Gravity
• Nonrelativistic fermions with holographic interactions and the unitary Fermi gas
• Non-Equilibrium Critical Phenomena From Probe Brane Holography in Schrödinger Spacetime
• On Pulsating Strings in Schrödinger Backgrounds
• SUSY Enhancements in (0,4) Deformations of AdS_3/CFT_2
• Flows to Schrodinger Geometries
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• Generalized Massive Gravity and Galilean Conformal Algebra in two dimensions
• Anisotropic conformal Carroll field theories and their gravity duals
• Gauss-Bonnet black holes in a special anisotropic scaling spacetime
• Hyperscaling violating Schrodinger black holes in Einstein-Maxwell-scalar theory
• Effects of high-order operators in non-relativistic Lifshitz holography
• Hamiltonian analysis for Lifshitz type Fields
• About the Non Relativistic Structure of the AdS/CFT Superalgebras
• Status of Superstring and M-Theory
• Recent Results in AdS/QCD
• Quantum mechanical observer and superstring/M theory
• Gravity Dual for Very Special Conformal Field Theories in type IIB Supergravity
• Supersymmetric Solutions in Four-Dimensional Off-Shell Curvature-Squared Supergravity
• Conformal symmetry in damped Pais-Uhlenbeck oscillator
• Schrödinger Holography with $z=2$
• Lifshitz hydrodynamics at generic $z$ from a moving black brane
• N=1,2,3 l-conformal Galilei superalgebras
• Holographic entanglement entropy for $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• Conformal Symmetry in nuclear structure
• Galilean Geometry in Condensed Matter Systems
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Towards a Gravity Dual for the Large Scale Structure of the Universe
• Three-dimensional non-relativistic Hietarinta supergravity
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter
• Correspondence between the contracted BTZ solution of cosmological topological massive gravity and two-dimensional Galilean conformal algebra
• A pedagogical review of gravity as a gauge theory
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• Perfect fluid coupled to a solenoidal field which enjoys the l-conformal Galilei symmetry
• Beyond AdS Space-times, New Holographic Correspondences and Applications
• Higher spin holography with Galilean symmetry in general dimensions
• On non-relativistic $Q\bar{Q}$ potential via Wilson loop in Galilean space-time
• Weyl Anomaly in NonRelativistic CFTs
• Holographic Phase Transitions in (2+1)-dimensional black hole spacetimes in NMG
• RG flows and cascades of $Li{f}_4^{(2)}\times S^1\times S^5$ vacua
• Characterization of three-dimensional Lorentzian metrics that admit four Killing vectors
• Note About Hamiltonian Dynamics of String in Non-Relativistic D3-Brane Background
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
• Critical points of WAdS/CFT and higher-curvature gravity
• Holographic Fisher Information Metric in Schrödinger Spacetime
• Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory
• Strange metals at finite 't Hooft coupling
• Conformal quantum mechanics and Fick-Jacobs equation
• Quantum Chaos of Unitary Fermi Gases in Strong Pairing Fluctuation Region
• From Equilibrium to Transport Properties of Strongly Correlated Fermi Liquids
• Spread of Entanglement in Non-Relativistic Theories
• Penrose Limit and Non-relativistic geometries
• Correlation functions for Galilean conformal invariant field theory
• Schrödinger Spacetimes with Screen and Reduced Entanglement
• The Schwarzschild/CFT Correspondence: Weyl Rescaled Case
• A+2n compound nuclei and the unitary limit in nuclear physics
• Non-relativistic entanglement entropy from Horava gravity
• Holographic stress tensor of colored Lifshitz spacetimes and hairy black holes
• Exact Solutions in Weyl-Cubed Gravity
• Extended Bargmann FDA and non-relativistic gravity
• Hyperscaling violating Lifshitz holography
• Developments in non-relativistic field theory and complexity
• Strongly Interacting Fermi Gases: Hydrodynamics and Beyond
• Observers and the AdS/CFT correspondence
• AdS Bubbles, E$p$-branes and Entanglement
• Anisotropic scaling non-relativistic holography: a symmetry perspective
• Hidden symmetries and nonlinear (super)algebras
• Fractional Galilean Symmetries
• Ground State Instability in Non-relativistic QFT and Euler-Heisenberg Lagrangian via Holography
• Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure
• Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions
• Critical scaling of the AC conductivity and momentum dissipation
• Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension
• Scale without Conformal Invariance in bottom-up Holography
• Null reduction and dynamical realization of Carrollian conformal symmetries
• Cosmological New Massive Gravity and Galilean Conformal Algebra in 2-dimensions
• A (1+1)-dimensional Lifshitz Weyl Anomaly From a Schr$\ddot{\mathrm{o}}$dinger-invariant Non-relativistic Chern-Simons Action
• Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
• Non-Abelian gauge theories invariant under diffeomorphisms
• Exploring Lovelock theory moduli space for Schroedinger solutions