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arXiv · 2410.19711

How Einstein's Equation Emerges From CFT$_2$

Xin Jiang·Peng Wang·Houwen Wu·Haitang Yang
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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$_2$ is precisely three dimensional Einstein's equation. We establish a profound relation between the cosmological constant and CFT$_2$ entanglement entropy. Thus entanglement entropies induce internal gravitational geometries in CFT$_2$. Extracting the dual metric from an entanglement entropy becomes a straightforward procedure. Remarkably, we discover that the renormalization group equation is a geometric identity.

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Xin Jiang, Peng Wang, Houwen Wu, Haitang Yang. 2024-10-25. How Einstein's Equation Emerges From CFT$_2$. https://doi.org/10.1103/zg5x-34mn

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