Discrete scale invariance in holography revisited

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 $AdS_5$ appear to be broken to an isometry group describing a discretely scale invariant and Poincar\'e 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 $AdS_5$ 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.