Timelike Entanglement Entropy in Higher Curvature Gravity

TL;DR

This work analyzes holographic timelike entanglement entropy within Lovelock gravity, focusing on how higher-curvature corrections and excited states alter the entanglement structure. Using complex extremal surfaces and perturbative expansions around Einstein gravity, it reveals that vacuum contributions acquire dimension-dependent imaginary parts while excitations contribute only to the real part, and that timelike entanglement entropy and spacelike entanglement entropy are related by systematic analytic-continuation relations. The study spans five-dimensional Gauss-Bonnet gravity and general d+1 dimensional Lovelock theories, including hyperbolic subsystems where imaginary contributions arise in all dimensions. A key outcome is a clear mapping between timelike and spacelike EE across curvature corrections, with vacuum terms tied to analytic continuation and excitation coefficients governed by dimension-dependent rational factors. These results shed light on the role of higher-curvature interactions in holographic timelike entanglement and its relation to vacuum and excited-state contributions, while outlining renormalization considerations and open questions about surface selection in complex geometries.

Abstract

This work investigates holographic timelike entanglement entropy in higher curvature gravity, with a particular focus on Lovelock theories and on the role of excited states. For strip subsystems, higher-curvature terms are found to affect the imaginary part of the entropy in a dimension-dependent manner, while excited states contribute solely to the real part. For the cases analyzed, spacelike and timelike entanglement entropies exhibit proportional relations: vacuum contributions differ by universal phase factors, while excitation contributions are linked by dimension-dependent rational coefficients. For hyperbolic subsystems, the timelike entanglement entropy computed via complex extremal surfaces is shown to agree with results obtained through analytic continuation, with imaginary contributions appearing in all dimensions. Higher-curvature corrections are explicitly calculated in five- and $(d+1)$-dimensional Gauss-Bonnet gravity, illustrating the applicability of the complex surface prescription to general Lovelock corrections. These results provide a controlled setting to examine the influence of higher-curvature interactions on holographic timelike entanglement entropy, and clarify its relation to vacuum and excited-state contributions.