Discrete scale invariance in holography revisited

Abstract

In 2013, Balasubramanian presented a 5+1 dimensional holographic toy model that allows for an exact solution to Einstein's equations in the bulk in which the isometries of $Ad{S}_5$ appear to be broken to an isometry group describing a discretely scale invariant and Poincaré invariant setup [arXiv:1301.6653]. In this paper, we investigate this solution in more detail. By analytically solving the Killing equations, we prove that the full $Ad{S}_5$ isometry group is still present, although in a somewhat hidden way. We will also comment on the prospects of finding other holographic bottom up toy models which allow for solutions with discrete scale invariance or scale invariance without conformal invariance in the future.

18 pages, 1 figure, v2: Minor improvements. This is the accepted version of the following article: Fortsch.Phys. 66 (2018) no.3, 1700093, which has been published in final form at https://doi.org/10.1002/prop.201700093

References in corpus (9)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Critical Exponents of Extremal Kerr Perturbations
• Efimov physics from a renormalization group perspective
• Boomerang RG flows with intermediate conformal invariance
• Critical behavior of the black hole / black string transition
• A simple test for spacetime symmetry
• Gravity duals of cyclic RG flows, with strings attached

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• A smeared quantum phase transition in disordered holography
• Spectral dimensions and dimension spectra of quantum spacetimes
• Critical and near-critical relaxation of holographic superfluids
• Discrete scale invariance in holography and an argument against the complexity=action proposal
• Scale without Conformal Invariance in bottom-up Holography