Quantum corrected black hole microstates and entropy

We extend the semiclassical black hole microstate construction to include quantum corrections to the microscopic entropy using a doubly holographic model of black holes. Specifically, we consider a double-sided black hole on a JT brane with holographic matter, coupled to a pair of holographic CFTs on the asymptotic boundaries. The dimension of the Hilbert space spanned by the microstates of this doubly holographic black hole is given by the exponentiated entropy, which is equal to the sum of the quantum-corrected thermodynamic entropies of the left and right black holes. Importantly, the quantum-corrected thermodynamic entropy is shown to be equal to the generalised entropy of the eternal black hole, and thus can be interpreted as quantifying the entanglement between the two asymptotic boundaries.