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**1 - 4**of**4**### Lifshitz Field Theories at Non-Zero Temperature

- Hydrodynamics and Gravity, JHEP 1403 (2014) 029, [arXiv:1309.6794

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### UvA-DARE (Digital Academic Repository) Lifshitz from AdS at finite temperature and top down model

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### Lifshitz holography: The whole shebang

"... Abstract: We provide a general algorithm for constructing the holographic dictionary for any asymp-totically 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], that are ..."

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Abstract: We provide a general algorithm for constructing the holographic dictionary for any asymp-totically 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], that are compat-ible 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 [2], 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.