cid 6cdac17ebe1cacba37e21aff3500006fe0a78426393af7229070322c6bc19186 · original · open access · via openalex
Title: Lifshitz holography: the whole shebang Authors: Wissam A Chemissany; Ioannis Papadimitriou Venue: Journal of High Energy Physics Year: 2015 Canonical: doi:10.1007/jhep01(2015)052 URL: https://doi.org/10.1007/jhep01(2015)052 Collector: openalex OA: true 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 z and θ, as well as the vector hyperscaling violating exponent [1, 2], 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 [3], 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 z 1 and θ 0 corresponding to a marginal deformation shifting the vector hyperscaling violating parameter and we present an example where the conformal anomaly contains the only z = 2 conformal invariant in d = 2 with four spatial derivatives.