Emergent AdS3 and BTZ Black Hole from Weakly Interacting Hot 2d CFT

TL;DR

This paper demonstrates how weakly interacting 2D hyperKähler sigma models can give rise to emergent AdS3 and BTZ black hole geometries through instanton moduli space analysis, linking field theory to holographic spacetime.

Contribution

It introduces a novel approach to emergent holography using instanton moduli space and Hitchin's metric in a 2D sigma model, revealing AdS3 and BTZ geometries.

Findings

Emergent geometry at zero temperature is AdS3.

Finite temperature instantons map to zero temperature via conformal transformation.

Emergent geometry at finite temperature is the BTZ black hole.

Abstract

We investigate emergent holography of weakly coupled two-dimensional hyperK\"ahler sigma model on cotangent bundle of (N-1)-dimensional complex projective space at zero and finite temperature. The sigma model is motivated by the spacetime conformal field theory dual to the near-horizon geometry of Q1 D1-brane bound to Q5 D5-brane wrapped on four-torus times circle, where N = Q1*Q5. The sigma model admits nontrivial instanton for all N greater than or equal to 2, which serves as a local probe of emergent holographic spacetime. We define emergent geometry of the spacetime as that of instanton moduli space via Hitchin's information metric. At zero temperature, we find that emergent geometry is AdS3. At finite temperature, time-periodic instanton is mappable to zero temperature instanton via conformal transformation. Utilizing the transformation, we show that emergent geometry is precisely that of the non-extremal, non-rotating BTZ black hole.