Replica Trick (Gravity)

Definition

The gravitational replica trick computes Rényi entropies $S_n=(1-n{)}^{-1}\log (Z_n/Z_1^n)$ as ratios of bulk partition functions on $n$-fold replicated geometries with conical singularities along the entangling surface; the analytic continuation $n\to 1$ recovers the von Neumann entropy and (Lewkowycz–Maldacena) gives the RT/HRT formula. Replica wormholes — connected bulk saddles dominating for evaporating black holes — are responsible for the Page curve.

Role in Research

The gravitational replica trick appears at Sem II Wks 4 and 10. It bridges the clean RT formula (static, geometric) to the black-hole information program (where replica wormholes are essential for restoring unitarity and producing the descending branch of the page-curve).

Relations

• ryu-takayanagi-formula — the Lewkowycz-Maldacena derivation of RT is the replica trick applied to static geometries.
• quantum-extremal-surfaces — replica wormholes provide the path-integral foundation of the QES prescription.
• page-curve — replica wormholes are responsible for the late-time decrease of Hawking radiation entropy.

Papers

• Lewkowycz–Maldacena 2013, arXiv:1304.4926.
• Almheiri–Hartman–Maldacena–Shaghoulian–Tajdini 2019, arXiv:1911.12333.
• Penington–Shenker–Stanford–Yang 2019, arXiv:1911.11977.

Notes

Course coverage: Lecture 16 (replicas and twist fields) and Lecture 27 (replica wormholes).