Three Dimensional Pure Gravity and Generalized Hecke Operators
arXiv:2004.04424 · doi:10.1007/JHEP09(2020)083
Abstract
In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into physically viable candidate partition functions. We explicitly detail the list of holomorphic and anti-holomorphic functions that serve as candidates for chiral and anti-chiral partition functions and note that modular covariance is only consistent with such functions when the left (resp. right) central charge is an integer multiple of 8, . We then find related constraints on the symmetry group of the corresponding topological, Chern-Simons, theory in the bulk of AdS. The symmetry group of the theory can be one of two choices: either or its three-fold diagonal cover. We introduce the generalized Hecke operators which map the modular covariant functions to the modular covariant functions. With these mathematical results, we obtain conjectural partition functions for extremal CFT2s, and the corresponding microcanonical entropies, when the chiral central charges are multiples of eight. Finally, we compute subleading corrections to the Beckenstein-Hawking entropy in the bulk gravitational theory with these conjectural partition functions
arXiv comment20 pages
References in corpus (29)
- Gauge Theory Correlators from Non-Critical String Theory
- The Black Hole in Three Dimensional Space Time
- Geometry of the 2+1 Black Hole
- Black Hole Entropy from Near-Horizon Microstates
- Quantum Gravity Partition Functions in Three Dimensions
- Logarithmic Corrections to Black Hole Entropy from the Cardy Formula
- Chiral Gravity in Three Dimensions
- Meromorphic c=24 Conformal Field Theories
- Chiral Gravity, Log Gravity and Extremal CFT
- A Universal Inequality for CFT and Quantum Gravity
- Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
- Spacetime structure near generic horizons and soft hair
- Poincare Series, 3D Gravity and CFT Spectroscopy
- An Exact Black Hole Entropy Bound
- Lightcone Modular Bootstrap and Pure Gravity
- Sphere Packing and Quantum Gravity
- Exact Results for the BTZ Black Hole
- Modular differential equations and null vectors
- Constraints on extremal self-dual CFTs
- Fast Conformal Bootstrap and Constraints on 3d Gravity
- Analytic Functional Bootstrap for CFTs in
- Beyond Logarithmic Corrections to Cardy Formula
- On Quantization of AdS3 Gravity I: Semi-Classical Analysis
- Interpolating Between Asymptotic and Near Horizon Symmetries
- Moonshine, Superconformal Symmetry, and Quantum Error Correction
- Three-dimensional AdS gravity and extremal CFTs at c=8m
- Non-chiral 2d CFT with integer energy levels
- Four-Dimensional Entropy from Three-Dimensional Gravity
- Chiral Modular Bootstrap