Lifshitz holography: The whole shebang
Wissam Chemissany, Ioannis Papadimitriou

TL;DR
This paper develops a comprehensive method for constructing the holographic dictionary for Lifshitz and hyperscaling violating backgrounds, enabling detailed analysis of dual field theories with non-relativistic scaling and anisotropic features.
Contribution
It introduces a recursive algorithm for solving the radial Hamilton-Jacobi equation in general Lifshitz holography models, including hyperscaling violation, and derives all holographic data and counterterms.
Findings
Derived Fefferman-Graham expansions for Lifshitz backgrounds
Identified Ward identities and holographic renormalization counterterms
Presented exact solutions with specific dynamical and hyperscaling exponents
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…
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