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Related Experiment Video

Updated: Oct 10, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

Emergent Einstein Equation in p-adic Conformal Field Theory Tensor Networks.

Lin Chen^1,2,3, Xirong Liu^1,2,3, Ling-Yan Hung^1,2,3,4

¹State Key Laboratory of Surface Physics, Fudan University, 200433 Shanghai, China.

Physical Review Letters

|December 10, 2021

Summary

We explore tensor networks for p-adic conformal field theory partition functions. This study shows deformed Bruhat-Tits tree geometry satisfies an emergent graph Einstein equation, linking geometry to physics.

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Area of Science:

Theoretical Physics
High Energy Physics
Mathematics

Background:

Tensor networks provide a framework for studying quantum field theories.
P-adic conformal field theories (CFTs) offer a novel approach to understanding physical phenomena.
Bruhat-Tits (BT) trees are mathematical structures with applications in theoretical physics.

Purpose of the Study:

To investigate the relationship between tensor networks and deformed Bruhat-Tits tree geometries.
To demonstrate the emergence of a graph Einstein equation from this setup.
To connect mathematical and physical definitions of graph curvature.

Main Methods:

Utilizing tensor networks to describe p-adic CFT partition functions.
Analyzing boundary conditions of the tensor network on a deformed BT tree.
Comparing emergent graph Einstein equations with bulk effective matter actions.
Examining the emergence of graph curvature definitions.

Main Results:

The deformed Bruhat-Tits tree geometry satisfies an emergent graph Einstein equation.
This emergent equation is consistent with the bulk effective matter action in the perturbative limit.
Mathematical and physical definitions of graph curvature naturally emerge from consistency requirements.

Conclusions:

The study establishes a novel connection between tensor networks, p-adic CFTs, and emergent gravitational dynamics.
The findings suggest that tensor networks can encode gravitational physics.
This work opens new avenues for understanding gravity in more general tensor network contexts.