Holographic timelike entanglement and subregion complexity with scalar hair

Abstract

We investigate the holographic timelike entanglement entropy (HTEE) and timelike subregion complexity of a thermal CFT${}_d$ deformed by a relevant scalar operator ${\varphi }_0$, 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 $\Delta t$. 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 $\Delta t$. At small $\Delta t$, 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.

42 pages, 11 figures, v3 matches the published version

References in corpus (27)

• Complexity and Shock Wave Geometries
• On Volumes of Subregions in Holography and Complexity
• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Timelike entanglement entropy
• Holographic Entanglement Entropy in Insulator/Superconductor Transition
• Diving into a holographic superconductor
• Gravitational duals to the grand canonical ensemble abhor Cauchy horizons
• Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
• No Inner-Horizon Theorem for Black Holes with Charged Scalar Hairs
• Holographic flows from CFT to the Kasner universe
• On holographic time-like entanglement entropy
• Time-like Entanglement Entropy in AdS/BCFT
• Trans-IR Flows to Black Hole Singularities
• Geometric Interpretation of Timelike Entanglement Entropy
• Temporal Entanglement Entropy as a probe of Renormalization Group Flow
• On subregion action complexity in AdS${}_3$ and in the BTZ black hole
• Kasner interiors from analytic hairy black holes
• Entanglement Entropy of Free Fermions in Timelike Slices
• Shock waves, black hole interiors and holographic RG flows
• Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation
• Holographic Timelike Entanglement Entropy from Rindler Method
• Diving into a holographic multi-band superconductor
• Relation between time- and spacelike entanglement entropy
• Diving inside holographic metals
• Scrambling in charged hairy black holes and the Kasner interior
• Duality of Ryu-Takayanagi surfaces inside and outside the horizon
• Stationary Solution to Charged Hairy Black Hole in AdS4: Kasner Interior, Rotating Shock Waves, and Fast Scrambling