How Einstein's Equation Emerges From CFT$_2$
Abstract
The {\it finiteness} of the entanglement entropies between disjoint subsystems enables us to show that, the dynamical equation of the entanglement entropy in CFT is precisely three dimensional Einstein's equation. We establish a profound relation between the cosmological constant and CFT entanglement entropy. Thus entanglement entropies induce internal gravitational geometries in CFT. Extracting the dual metric from an entanglement entropy becomes a straightforward procedure. Remarkably, we discover that the renormalization group equation is a geometric identity.
Cite
@article{arxiv.2410.19711,
title = {How Einstein's Equation Emerges From CFT$_2$},
author = {Xin Jiang and Peng Wang and Houwen Wu and Haitang Yang},
journal= {arXiv preprint arXiv:2410.19711},
year = {2025}
}
Comments
V5: Accepted for publication in PRD Letter. Used an entirely different logic from V4 to emphasize the purely CFT-based derivation of Einstein's equation. Added an appendix to show the equivalence between EoP and EE of annular CFT. But derivations of V4 are easier to follow