Entanglement entropy for the black 0-brane

We analyze the entanglement entropy between the black 0-brane solution to supergravity and its Hawking radiation. The black 0-brane admits a dual gauge theory description in terms of the matrix model for M-theory, named Banks Fischler Shenker Susskind (BFSS) theory, which is the theory of open strings on a collection of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>N</a:mi></a:mrow></a:math> <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>D</c:mi><c:mn>0</c:mn></c:msub></c:math>-branes. Recent studies of the model have highlighted a mechanism of black hole evaporation for this system, based on the chaotic nature of the theory and the existence of flat directions. This paper further explores this idea, through the computation of the von Neumann entropy of Hawking radiation. In particular, we show that the expected Page curve is indeed reproduced, consistently with a complete recovery of information after the black hole has fully evaporated. A pivotal step in the computation is the definition of a Hilbert space that allows for a quantum mechanical description of partially evaporated black holes. We find that the entanglement entropy depends on the choice of a parameter, which can be interpreted as summarizing the geometric features of the black hole, such as the size of the resolved singularity and the size of the horizon. Published by the American Physical Society 2024