Emergent AdS3 and BTZ Black Hole from Weakly Interacting Hot 2d CFT
arXiv:hep-th/0604102 · doi:10.1088/1126-6708/2006/07/023
Abstract
We investigate emergent holography of weakly coupled two-dimensional hyperKähler 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.
arXiv comment12 pages, no figure, JHEP.cls; v2. typos corrected
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- AdS gravastar and bulk-cone singularities
- Information metric from a linear sigma model
- A deconstruction lattice description of the D1/D5 brane world-volume gauge theory
- Interplay between the small and the large scale structure of spacetime