paper

Lifshitz holography: The whole shebang

arXiv:1408.0795 · doi:10.1007/JHEP01(2015)052

Abstract

We provide a general algorithm for constructing the holographic dictionary for any asymptotically locally Lifshitz background, with or without hyperscaling violation, and for any values of the dynamical exponents and , as well as the vector hyperscaling violating exponent, that are compatible with the null energy condition. The analysis is carried out for a very general bottom up model of gravity coupled to a massive vector field and a dilaton with arbitrary scalar couplings. The solution of the radial Hamilton-Jacobi equation is obtained recursively in the form of a graded expansion in eigenfunctions of two commuting operators, which are the appropriate generalization of the dilatation operator for non scale invariant and Lorentz violating boundary conditions. The Fefferman-Graham expansions, the sources and 1-point functions of the dual operators, the Ward identities, as well as the local counterterms required for holographic renormalization all follow from this asymptotic solution of the radial Hamilton-Jacobi equation. We also find a family of exact backgrounds with and corresponding to a marginal deformation shifting the vector hyperscaling violating parameter and we present an example where the conformal anomaly contains the only conformal invariant in with four spatial derivatives.

arXiv comment83 pages, 1 figure

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