Timelike Entanglement Entropy in Higher Curvature Gravity

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.