Abstract
We advance two alternative proposals for the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity. The first construction involves the extremization of an algebraic sum of the generalized Renyi entropies of order half. The second proposal involves the extremization of the sum of the effective entanglement negativity of quantum matter fields and the backreacted area of a cosmic brane spanning the entanglement wedge cross section which also extremizes the generalized Renyi reflected entropy of order half. These proposals are utilized to obtain the island contributions to the entanglement negativity of various pure and mixed state configurations involving the bath systems coupled to extremal and non-extremal black holes in JT gravity demonstrating an exact match with each other. Furthermore, the results from both the proposals match precisely with the island contribution to half the Renyi reflected entropy of order half providing a strong consistency check. We then allude to a possible doubly holographic picture of our island proposals and provide a derivation of the first proposal by determining the corresponding replica wormhole contributions.
Highlights
A.1 Entanglement negativity of the thermofield double (TFD) state dual to an eternal black hole in JT gravity
The above mentioned holographic proposals lead to the significant question concerning the island construction for the entanglement negativity. We address this extremely interesting issue by proposing two alternative constructions to determine the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity
Inspired by [91], we propose that the island contribution to the entanglement negativity of a quantum field theory coupled to semiclassical gravity is obtained by extremizing half the generalized Renyi reflected entropy of order half, which corresponds to a different analytic continuation of eq(37)
Summary
The black hole information loss paradox is one of the most intriguing puzzles of modern theoretical physics [1,2,3,4,5]. We address this extremely interesting issue by proposing two alternative constructions to determine the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity. We apply our proposals to compute the island contributions to the entanglement negativity of several pure and mixed state configurations in non-gravitating bath systems coupled to extremal and non-extremal black holes in Jackiw-Teitelboim (JT) gravity coupled to matter described by a large-c CFT2.
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