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Presented By: Leinweber Center for Theoretical Physics

Brown Bag Seminar | Near-Extremal Black Hole Entropies from Replica Matrices

Sergio Hernandez-Cuenca (MIT)

A generic pathology one encounters when computing the thermal entropy of a black hole is that it becomes negatively divergent as the temperature goes to zero, and only those whose extremal limit preserve some supersymmetry yield a sensible low-temperature entropy. The physics relevant to these phenomena are all captured by Jackiw-Teitelboim theories of gravity, which have been rather explicitly shown to be dual to various matrix ensembles. The issues and features mentioned above can all be precisely understood from this perspective: traditional gravitational calculations are computing annealed quantities, which give inherently wrong approximations near extremality.
We use the matrix integral formulation to show how quenched quantities do in fact behave sensibly and yield non-negative entropies at all temperatures. By using a suitable replica trick, this is done for a completely general matrix ensemble, thus settling the question for any black hole whose near-extremal spectrum is captured by such ensembles. Crucially, this result only requires working perturbatively to leading order in the size of the matrices, which hints at the possibility of an analogous semiclassical gravitational computation where one just needs to account for wormhole contributions appropriately (and not for doubly non-perturbative effects in 1/G).

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