Lodged in the throat: Internal infinities and AdS/CFT

TL;DR

This paper explores the AdS3/CFT2 correspondence for extreme BTZ black holes with internal infinities, proposing a product CFT description and analyzing the dual state in a simplified model.

Contribution

It introduces a novel product CFT framework for describing spacetimes with internal infinities in AdS3/CFT2 and analyzes the dual state of the extreme BTZ black hole.

Findings

The dual CFT state is a quotient of the vacuum state.

The dual state resides in a product CFT structure.

The approach provides insights into entanglement entropy in such geometries.

Abstract

In the context of AdS3/CFT2, we address spacetimes with a certain sort of internal infinity as typified by the extreme BTZ black hole. The internal infinity is a null circle lying at the end of the black hole's infinite throat. We argue that such spacetimes may be described by a product CFT of the form CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary while CFT-L is associated with the null circle. Our particular calculations analyze the CFT dual of the extreme BTZ black hole in a linear toy model of AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dual CFT state is a corresponding quotient of the CFT vacuum state. This state turns out to live in the aforementioned product CFT. We discuss this result in the context of general issues of AdS/CFT duality and entanglement entropy.