Holographic timelike entanglement and subregion complexity with scalar hair
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913052889186304 |
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| author | Prihadi, Hadyan Luthfan Al-Faritsi, Muhammad Alifaldi Ramadhan Firdaus, Rafi Rizqy Khairunnisa, Fitria Sarwono, Yanoar Pribadi Zen, Freddy Permana |
| author_facet | Prihadi, Hadyan Luthfan Al-Faritsi, Muhammad Alifaldi Ramadhan Firdaus, Rafi Rizqy Khairunnisa, Fitria Sarwono, Yanoar Pribadi Zen, Freddy Permana |
| contents | We investigate the holographic timelike entanglement entropy (HTEE) and timelike subregion complexity of a thermal CFT$_d$ deformed by a relevant scalar operator $ϕ_0$, dual to a hairy black hole in AdS$_{d+1}$. We employ the prescription of merging spacelike and timelike surfaces at the interior, constructing an extremal surface homologous to a boundary timelike subsystem with a time interval $Δt$. Consequently, this deformation breaks the invariance of the imaginary component of HTEE observed in pure AdS$_3$ and BTZ geometry, introducing a nontrivial dependence on $Δt$. At small $Δt$, we derive analytical expressions that are in agreement with numerical results, and observe partial consistency with analytic continuation to temporal or spacelike entanglement entropy at the level of the near-boundary expansion. However, analytic continuation of CFT temporal entanglement entropy fails to reproduce the HTEE calculations under boundary deformation, even in $d=2$. Furthermore, we extend the numerical calculations to higher dimensions ($d=3$). In addition, we study holographic timelike subregion complexity within the complexity=volume conjecture and find that it remains real-valued, providing a complementary geometric probe of the black hole interior. In particular, for the BTZ black hole, we analytically show that the UV-finite term of the subregion complexity receives its entire contribution from the interior region alone. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_18310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holographic timelike entanglement and subregion complexity with scalar hair Prihadi, Hadyan Luthfan Al-Faritsi, Muhammad Alifaldi Ramadhan Firdaus, Rafi Rizqy Khairunnisa, Fitria Sarwono, Yanoar Pribadi Zen, Freddy Permana High Energy Physics - Theory General Relativity and Quantum Cosmology We investigate the holographic timelike entanglement entropy (HTEE) and timelike subregion complexity of a thermal CFT$_d$ deformed by a relevant scalar operator $ϕ_0$, dual to a hairy black hole in AdS$_{d+1}$. We employ the prescription of merging spacelike and timelike surfaces at the interior, constructing an extremal surface homologous to a boundary timelike subsystem with a time interval $Δt$. Consequently, this deformation breaks the invariance of the imaginary component of HTEE observed in pure AdS$_3$ and BTZ geometry, introducing a nontrivial dependence on $Δt$. At small $Δt$, we derive analytical expressions that are in agreement with numerical results, and observe partial consistency with analytic continuation to temporal or spacelike entanglement entropy at the level of the near-boundary expansion. However, analytic continuation of CFT temporal entanglement entropy fails to reproduce the HTEE calculations under boundary deformation, even in $d=2$. Furthermore, we extend the numerical calculations to higher dimensions ($d=3$). In addition, we study holographic timelike subregion complexity within the complexity=volume conjecture and find that it remains real-valued, providing a complementary geometric probe of the black hole interior. In particular, for the BTZ black hole, we analytically show that the UV-finite term of the subregion complexity receives its entire contribution from the interior region alone. |
| title | Holographic timelike entanglement and subregion complexity with scalar hair |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.18310 |