Trans-IR flows to black hole singularities

Abstract

We study analytic continuations of holographic renormalization group (RG) flows beyond their infrared (IR) fixed points. Such ``trans-IR'' flows are a natural framework for describing physics inside of black holes. First, we construct a monotonic holographic $a$-function which counts degrees of freedom along a trans-IR flow. Using this function, we argue that the degrees of freedom ``thin out'' and vanish when flowing to a trans-IR endpoint, represented by a Kasner singularity. We then recast well-studied quantum information probes in the language of trans-IR flows, finding that entanglement and complexity from volume generally fail to fully probe the trans-IR while 2-point correlations and complexity from action generally do so in a complementary manner.