Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
Entanglement and alpha entropies for a massive Dirac field in two dimensions
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abstract
We present some exact results about universal quantities derived from the local density matrix, for a free massive Dirac field in two dimensions. We first find the trace of powers of the density matrix in a novel fashion, which involves the correlators of suitable operators in the sine-Gordon model. These, in turn, can be written exactly in terms of the solutions of non-linear differential equations of the Painlev\'e V type. Equipped with the previous results, we find the leading terms for the entanglement entropy, both for short and long distances, and showing that in the intermediate regime it can be expanded in a series of multiple integrals. The previous results have been checked by direct numerical calculations on the lattice, finding perfect agreement. Finally, we comment on a possible generalization of the entanglement entropy c-theorem to the alpha-entropies.
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A hierarchy of approximations to the mutual information in CFTs is derived from modular flow and two-point functions of primaries, providing a high-precision formula for arbitrary ball separations that supersedes previous long-distance expansions.
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.
citing papers explorer
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Replica Wormholes and the Entropy of Hawking Radiation
Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
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Mutual Information from Modular Flow in General CFTs
A hierarchy of approximations to the mutual information in CFTs is derived from modular flow and two-point functions of primaries, providing a high-precision formula for arbitrary ball separations that supersedes previous long-distance expansions.
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Symmetry-Resolved Entanglement Entropy from Heat Kernels
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
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Lectures on entanglement entropy in field theory and holography
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.