We can give two very different descriptions of the evolution of a black hole formed from the collapse of a star. On the one hand, we have an "effective" description from quantum field theory on the black hole geometry: in this picture, the time-evolution appears to violate unitarity, leading to information loss. On the other hand, in its "fundamental" description, the black hole can be treated as a chaotic quantum many-body system with unitary time-evolution. It was previously expected that going from the effective to the fundamental picture would require highly non-trivial inputs from string theory. However, it has recently been found that simple prescriptions called islands and replica wormholes allow us to use the effective description to deduce the unitary time-evolution in the fundamental description.
In this lecture series, I will present two ways of understanding the origin of these prescriptions. In one perspective, based on arXiv: 2008.01089, the black hole information loss paradox can be seen as an example of an apparent paradox in any thermalizing quantum many-body
system. The replica wormhole prescription then comes from the universal resolution of this paradox in quantum many-body systems. In the second perspective, based on arXiv: 2207.06536, we understand the island formula in terms of properties of the holographic map from the effective to the fundamental description. In contrast to the holographic map in setups without a black hole, this map is not an isometry, but still has certain error-correction properties which allow us to express quantities in the fundamental description using
those in the effective description.