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arXiv · 2205.07905

Defect extremal surfaces for entanglement negativity

Debarshi Basu·Himanshu Parihar·Vinayak Raj·Gautam Sengupta
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Abstract

We propose a doubly holographic version of the semi-classical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the AdS bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semi-classical island formula for the entanglement negativity is demonstrated in AdS$_3$/BCFT$_2$ framework. Furthermore, in the time-dependent AdS$_3$/BCFT$_2$ scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulae and obtain the analogues of the Page curves.

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Debarshi Basu, Himanshu Parihar, Vinayak Raj, Gautam Sengupta. 2022-05-16. Defect extremal surfaces for entanglement negativity. https://doi.org/10.1103/physrevd.108.106005

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