Interactions resolve state-dependence in a toy-model of AdS black holes

TL;DR

This paper demonstrates how interactions in a toy-model of AdS black holes resolve the state-dependence issue in describing black hole microstates, linking holography, scalar fields, and quantum mechanics.

Contribution

It introduces a solvable double well potential toy-model showing how interactions replace state-dependence in black hole microstate descriptions.

Findings

Interactions eliminate the need for state-dependent operators.

A naive number operator suggests a firewall, but proper state construction removes this.

The model connects holographic duals with quantum mechanical analogs.

Abstract

We show that the holographic description of a class of AdS black holes with scalar hair involves dual field theories with a double well effective potential. Black hole microstates have significant support around both vacua in the dual, which correspond to perturbative degrees of freedom on opposite sides of the horizon. A solvable toy-model version of this dual is given by a quantum mechanical particle in a double well potential. In this we show explicitly that the interactions replace the state-dependence that is needed to describe black hole microstates in a low energy effective model involving the tensor product of two decoupled harmonic oscillators. A naive number operator signals the presence of a firewall but a careful construction of perturbative states and operators extinguishes this.