Hyperscaling violating Lifshitz holography
Ioannis Papadimitriou

TL;DR
This paper develops a comprehensive holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds with arbitrary exponents, enabling better understanding of dual non-relativistic field theories.
Contribution
It provides a systematic method to construct the holographic dictionary for these backgrounds within a generic Einstein-Proca-Dilaton framework, including asymptotic expansions and Ward identities.
Findings
Constructed the holographic dictionary for Lifshitz backgrounds.
Derived Fefferman-Graham asymptotic expansions.
Established non-relativistic holographic Ward identities.
Abstract
We present an overview of the construction of the general holographic dictionary for asymptotically locally Lifshitz and hyperscaling violating Lifshitz backgrounds with arbitrary dynamical exponents and , compatible with the null energy condition, which was recently developed in [1,2]. A concrete definition of asymptotically locally Lifshitz and hyperscaling violating Lifshitz backgrounds is provided in the context of a generic bottom-up Einstein-Proca-Dilaton theory, and a systematic procedure for solving the radial Hamilton-Jacobi equation via a covariant expansion in eigenfunctions of two commuting operators is presented. The resulting asymptotic solution of the Hamilton-Jacobi equation is subsequently used to derive the full holographic dictionary, including the Fefferman-Graham asymptotic expansions and the non-relativistic holographic Ward identities.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Cosmology and Gravitation Theories · Noncommutative and Quantum Gravity Theories
