Hyperscaling violation : a unified frame for effective holographic theories

Abstract

We investigate systematic classifications of low energy and lower dimensional effective holographic theories with Lifshitz and Schrödinger scaling symmetries only using metrics in terms of hyperscaling violation ($\theta$) and dynamical ($z$) exponents. Their consistent parameter spaces are constrained by null energy and positive specific heat conditions, whose validity is explicitly checked against a previously known result. From dimensional reductions of many microscopic string solutions, we observe the classifications are tied with the number of scales in the original microscopic theories. Conformal theories do not generate a nontrivial $\theta$ for a simple sphere reduction. Theories with Lifshitz scaling with one scale are completely fixed by $\theta$ and $z$, and have a universal emblackening factor at finite temperature. Dimensional reduction of intersecting M2-M5 requires, we call, spatial anisotropic exponents ($♯$), along with $z$=1, $\theta$=0, because of another scale. Theories with Schrödinger scaling show similar simple classifications at zero temperature, while require more care due to an additional parameter being a thermodynamic variable at finite temperature.

1+63 pages, 12 figures, v2 : typos corrected, published version

References in corpus (32)

• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Effective Holographic Theories for low-temperature condensed matter systems
• Exploring improved holographic theories for QCD: Part II
• Non-relativistic holography
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• Holography of Dyonic Dilaton Black Branes
• Consistent supersymmetric Kaluza--Klein truncations with massive modes
• The geometry of Schrödinger symmetry in non-relativistic CFT
• On the spectrum of nonrelativistic AdS/CFT
• Holography for Schrodinger backgrounds
• Families of IIB duals for nonrelativistic CFTs
• Fermi surfaces and gauge-gravity duality
• 1/N Effects in Non-Relativistic Gauge-Gravity Duality
• Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries
• Holography of charged dilatonic black branes at finite temperature
• Supersymmetric solutions for non-relativistic holography
• Thermodynamics of Black Holes in Schroedinger Space
• On the Null Energy Condition and Causality in Lifshitz Holography
• Solutions of type IIB and D=11 supergravity with Schrodinger(z) symmetry
• Strange Metallic Behavior in Anisotropic Background
• Non-relativistic Branes
• The particle number in Galilean holography
• Entangled Dilaton Dyons
• Holography for chiral scale-invariant models
• On Holographic Entanglement Entropy of Charged Matter
• Charged Dilatonic Black Holes and their Transport Properties
• Strange Metallic Behaviour and the Thermodynamics of Charged Dilatonic Black Holes
• Aspects of Puff Field Theory
• Aging Logarithmic Conformal Field Theory : a holographic view
• Geometry and Phase Structure of Non-Relativistic Branes

Cited by in corpus (6)

• Thermodynamic Topology and Photon Spheres in the Hyperscaling violating black holes
• Quantum Fluctuations in Holographic Theories with Hyperscaling Violation
• High-dimensional Lifshitz-type spacetimes, universal horizons and black holes in Hořava-Lifshitz gravity
• Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation
• Formation of Fermi surfaces and the appearance of liquid phases in holographic theories with hyperscaling violation
• Holographic charge diffusion in non relativistic branes