Three dimensional origin of AdS₂ quantum gravity

We study AdS₂ quantum gravity with emphasis on consistency with results from AdS₃. We lift AdS₂ black holes to three dimensions and map fluctuations around the solutions. Comparison with near extremal BTZ are discussed, with due emphasis on global aspects. The results confirm that parameters like central charges and conformal weights computed directly in 2D are consistent with standard results in 3D. Applying our results to the thermodynamics of near extreme Kerr black holes, we show that AdS ₂ quantum gravity gives the correct central charge c = 12J, and the entropy of excitations above the extremal limit is captured correctly.