Lifshitz as a deformation of Anti-de Sitter

Abstract

We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. We show that the holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1 theory. Treating epsilon as a small expansion parameter we set up the holographic dictionary for Einstein-Proca models up to order epsilon^2 in three and four bulk dimensions. We explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent z=1+epsilon^2. We compute the two-point function of the conserved spin two current for the dual two-dimensional field theory and verify that it is Lifshitz invariant. Using only QFT arguments, we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we construct examples of such deformations.

70 pages; v2: references added and minor improvements

References in corpus (14)

• Gravity duals for non-relativistic CFTs
• Interactions and phase transitions on graphene's honeycomb lattice
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Universal hydrodynamics of non-conformal branes
• Holographic stress tensor for non-relativistic theories
• Lifshitz Solutions of D=10 and D=11 supergravity
• Lifshitz Gravity for Lifshitz Holography
• Constructing Lifshitz solutions from AdS
• Holography for Schrodinger backgrounds
• Lifshitz solutions in supergravity and string theory
• Non-relativistic holography from Horava gravity
• An alternative IIB embedding of F(4) gauged supergravity
• Electric field effect modulation of transition temperature, mobile carrier density and in-plane penetration depth in NdBa2Cu3O(7-delta) thin films
• Holography for chiral scale-invariant models

Cited by in corpus (31)

• Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
• 5D Rotating Black Holes and the nAdS${}_2$/nCFT${}_1$ Correspondence
• Lifshitz holography: The whole shebang
• Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
• Lifshitz Scale Anomalies
• Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity
• Pseudo-spontaneous $U(1)$ Symmetry Breaking in Hydrodynamics and Holography
• Warped Entanglement Entropy
• Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes
• The renormalization group flow in field theories with quenched disorder
• The renormalization group in quantum quenched disorder
• Lifshitz from AdS at finite temperature and top down models
• Entanglement and mutual information in two-dimensional nonrelativistic field theories
• A Massive Quasi-normal Mode in the Holographic Lifshitz Theory
• Lifshitz flows in IIB and dual field theories
• FRW cosmologies and hyperscaling-violating geometries: higher curvature corrections, ultrametricity, Q-space/QFT duality, and a little string theory
• An Hamilton-Jacobi formulation of anisotropic inflation
• Decrypting the warped black strings
• Holographic quenches towards a Lifshitz point
• Holographic Approach to Entanglement Entropy in Disordered Systems
• Holographic Entanglement Entropy in NMG
• Notes on the holographic Lifshitz theory
• Holographic Lifshitz flows
• Are there Goldstone bosons in $d\le z+1$ ?
• On black hole thermodynamics with a momentum relaxation
• Drude weight and Mazur-Suzuki bounds in holography
• Symmetry breaking in holographic theories with Lifshitz scaling
• Information theoretic measures for Lifshitz system
• Hamiltonian analysis for Lifshitz type Fields
• Towards a Gravity Dual for the Large Scale Structure of the Universe
• Effective Lifshitz black holes, hydrodynamics, and transport coefficients in fluid/gravity correspondence