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<p>In this article, we investigate the proposed duality between the island and the defect extremal surface (DES) prescriptions using the fine-grained entanglement entropy in Karch-Randall (KR) brane-world models with gravitating radiation baths. We consider the AdS<sub>3</sub> black string geometry and compute the entanglement entropy for radiation subsystems on an AdS<sub>2</sub> eternal black hole background using both the island and the DES prescriptions. We find an agreement between the two proposals for the island and the no-island phases, thus verifying the validity of the proposed duality. We further extend to a <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> deformed AdS<sub>3</sub> black string geometry with a cut-off and find consistent results for both phases. We finally plot and compare the Page curves for the undeformed and deformed scenarios, and discuss the modifications due to <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( T\overline{T} \)</EquationSource> </InlineEquation> deformation.</p>

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Entanglement, defects, and \( T\overline{T} \) on a black hole background

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  • 发表日期：

    2026年2月25日

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  • Ankur Dey

摘要

In this article, we investigate the proposed duality between the island and the defect extremal surface (DES) prescriptions using the fine-grained entanglement entropy in Karch-Randall (KR) brane-world models with gravitating radiation baths. We consider the AdS3 black string geometry and compute the entanglement entropy for radiation subsystems on an AdS2 eternal black hole background using both the island and the DES prescriptions. We find an agreement between the two proposals for the island and the no-island phases, thus verifying the validity of the proposed duality. We further extend to a T T ¯ \( T\overline{T} \) deformed AdS3 black string geometry with a cut-off and find consistent results for both phases. We finally plot and compare the Page curves for the undeformed and deformed scenarios, and discuss the modifications due to T T ¯ \( T\overline{T} \) deformation.