On Modular Invariance and 3D Gravitational Instantons
arXiv:hep-th/9903222 · doi:10.1103/PhysRevD.60.064012
Abstract
We study the modular transformation properties of Euclidean solutions of 3D gravity whose asymptotic geometry has the topology of a torus. These solutions represent saddle points of the grand canonical partition function with an important example being the BTZ black hole, and their properties under modular transformations are inherited from the boundary conformal field theory encoding the asymptotic dynamics. Within the Chern Simons formulation, classical solutions are characterised by specific holonomies describing the wrapping of the gauge field around cycles of the torus. We find that provided these holonomies transform in an appropriate manner, there exists an associated modular invariant grand canonical partition function and that the spectrum of saddle points naturally includes a thermal bath in as discussed by Maldacena and Strominger. Indeed, certain modular transformations can naturally be described within classical bulk dynamics as mapping between different foliations with a "time" coordinate along different cycles of the asymptotic torus.
14 pages, RevTeX, typos corrected, to appear in Phys. Rev. D
References in corpus (13)
- Gauge Theory Correlators from Non-Critical String Theory
- Black Hole Entropy from Near-Horizon Microstates
- AdS3 Black Holes and a Stringy Exclusion Principle
- What We Don't Know about BTZ Black Hole Entropy
- Boundary dynamics and the statistical mechanics of the 2+1 dimensional black hole
- Statistical Entropy and AdS/CFT Correspondence in BTZ Black Holes
- Conformal Field Theory, Geometry, and Entropy
- A note on covariant action integrals in three dimensions
- Embeddings of the Virasoro algebra and black hole entropy
- A Note on Einstein Gravity on AdS and Boundary Conformal Field Theory
- The Quantum Modular Group in (2+1)-Dimensional Gravity
- Twisted sectors in three-dimensional gravity
- AdS3 Gravitational Instantons from Conformal Field Theory