Generalized dilatation operator method for non-relativistic holography

Abstract

We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent $z$ and any value of the hyperscaling violation parameter $\theta$ compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton-Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.

6 pages; v2 references added, discussion of the algorithm and the holographic dictionary improved

References in corpus (25)

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Cited by in corpus (20)

• Lifshitz holography
• Lifshitz Space-Times for Schroedinger Holography
• Lifshitz holography: The whole shebang
• Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
• Counterterms, Kounterterms, and the variational problem in AdS gravity
• Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance
• Intermediate scalings in holographic RG flows and conductivities
• Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Two-point Functions in a Holographic Kondo Model
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation
• Hyperscaling-Violating Lifshitz hydrodynamics from black-holes: Part II
• Schrodinger Holography for z<2
• Hamilton-Jacobi Approach to Holographic Renormalization of Massive Gravity
• Disformal transformation in Newton-Cartan geometry
• Holographic renormalization by Hamilton-Jacobi formulation with generated ansatz
• On the Rényi entropy of Lifshitz and hyperscaling violating black holes
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
• Hyperscaling violating Lifshitz holography