Trans-IR Flows to Black Hole Singularities

TL;DR

This paper explores the extension of holographic RG flows beyond IR fixed points to describe black hole interiors, introducing a new a-function and analyzing quantum information probes in this trans-IR regime.

Contribution

It constructs a monotonic holographic a-function for trans-IR flows and analyzes how different quantum information measures probe black hole singularities.

Findings

Degrees of freedom vanish at trans-IR endpoints.

Entanglement and volume complexity often fail to probe trans-IR.

2-point correlations and action complexity can probe trans-IR in a complementary way.

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.