Timelike Entanglement in 2d CFT
A 2d CFT construction analytically continues replica twist correlators to timelike, time-ordered insertions and matches them to complex geodesics in 3d holography.
TL;DR — The abstract presents a 2d CFT formulation of timelike entanglement entropy and its Rényi extension via analytic continuation of replica twist correlators to time-ordered, timelike-separated insertions. In 3d holography, the semiclassical boundary correlator selects boundary-anchored complex geodesics, specifically the saddle with the smallest real part of the length. The construction extends to Rényi index n>1 with a vacuum complex cosmic-brane geometry, agrees with boundary calculations in named examples, differs from earlier AdS-Vaidya piecewise geodesic constructions while matching field theory, and fixes an imaginary entropy part quantized in units of cπ/6 by operator ordering.
Core contribution
The abstract’s central contribution is a field-theoretic formulation of timelike entanglement entropy and its Rényi extension in two-dimensional conformal field theory. The supported construction is precise at the abstract level: analytic continuation of replica twist correlators to time-ordered, timelike-separated insertions.
This revision does not add branch-cut details, replica-manifold geometry, operator dimensions, or explicit twist correlator formulas because those are not present in the supplied abstract.
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