Coset Construction for Duals of Non-relativistic CFTs

Abstract

We systematically analyze backgrounds that are holographic duals to non-relativistic CFTs, by constructing them as cosets of the Schrodinger group and variants thereof. These cosets G/H are generically non-reductive and we discuss in generality how a metric on such spaces can be determined from a non-degenerate H-invariant symmetric two-form. Applying this to the d=2 Schrodinger algebra, we reproduce the five-dimensional backgrounds proposed as duals of fermions at unitarity, and under reasonable physical assumptions, we demonstrate uniqueness of this background. The proposed gravity dual of the Lifshitz fixed-point, for which Galileian symmetry is absent, also fits into this organizational scheme and uniqueness of this background can also be shown.

12 pages; v2: typos corrected, references added

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Cited by in corpus (50)

• Jordanian deformations of the AdS_5xS^5 superstring
• Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent
• Holographic stress tensor for non-relativistic theories
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Yang-Baxter sigma models based on the CYBE
• Constructing Lifshitz solutions from AdS
• Integrability of classical strings dual for noncommutative gauge theories
• A Jordanian deformation of AdS space in type IIB supergravity
• Hybrid classical integrability in squashed sigma models
• Yangian symmetry in deformed WZNW models on squashed spheres
• Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries
• The classical origin of quantum affine algebra in squashed sigma models
• Supersymmetric IIB Solutions with Schrödinger Symmetry
• Schrödinger geometries arising from Yang-Baxter deformations
• Hidden Yangian symmetry in sigma model on squashed sphere
• Spatially isotropic homogeneous spacetimes
• Schrodinger Sigma Models and Jordanian Twists
• Non-integrability in non-relativistic theories
• A deformation of quantum affine algebra in squashed WZNW models
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• Integrability in dipole-deformed N=4 super Yang-Mills
• Yangians, S-matrices and AdS/CFT
• Super Galilean conformal algebra in AdS/CFT
• Lifshitz-like black brane thermodynamics in higher dimensions
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
• Exotic symmetry and monodromy equivalence in Schrodinger sigma models
• Non-relativistic metrics with extremal limits
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• Very Special Conformal Field Theories (VSCFT) and their holographic duals
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• Yang-Baxter invariance of the Nappi-Witten model
• Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds
• Schrödinger Manifolds
• Schrödinger Deformations of AdS_3 x S^3
• Aging and Holography
• Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
• Metrics with Galilean Conformal Isometry
• Universal time-dependent deformations of Schrodinger geometry
• Particle Number and 3D Schroedinger Holography
• Asymptotically Lifshitz Brane-World Black Holes
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Yang-Baxter deformations of Minkowski spacetime
• Lax pairs for deformed Minkowski spacetimes
• Deformations of $T^{1,1}$ as Yang-Baxter sigma models
• An Index for Quantum Integrability
• Asymptotically Schrödinger Space-Times
• Lax pairs on Yang-Baxter deformed backgrounds
• Yang-Baxter deformations and string dualities