Emergent Einstein Equation inp-adic Conformal Field Theory Tensor Networks,Physical Review Letters

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Emergent Einstein Equation inp-adic Conformal Field Theory Tensor Networks
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-11-23 , DOI: 10.1103/physrevlett.127.221602
Lin Chen _{1,

2,

3} , Xirong Liu _{1,

2,

3} , Ling-Yan Hung _{1,

2,

3,

4}

Affiliation

We take the tensor network describing explicit

p

-adic conformal field theory partition functions proposed in [L.-Y. Hung et al., J. High Energy Phys. 04 (2019) 170], and consider boundary conditions of the network describing a deformed Bruhat-Tits (BT) tree geometry. We demonstrate that this geometry satisfies an emergent graph Einstein equation in a unique way that is consistent with the bulk effective matter action encoding the same correlation function as the tensor network, at least in the perturbative limit order by order away from the pure BT tree. Moreover, the (perturbative) definition of the graph curvature in the mathematics [Y. Lin and S.-T. Yau, Tohoku Math. J. 63, 605 (2011); Y. Ollivier, J. Funct. Anal. 256, 810 (2009)] and physics [S. S. Gubser et al., J. High Energy Phys. 06 (2017) 157] literature naturally emerges from the consistency requirements of the emergent Einstein equation. This could provide new insights into the understanding of gravitational dynamics potentially encoded in more general tensor networks.

中文翻译：

涌现爱因斯坦方程 inp-adic 共形场论张量网络

我们采用描述显式的张量网络

p

-adic 共形场论分配函数在 [L.-Y. 洪等人。, J. 高能物理。04 ( 2019 ) 170]，并考虑描述变形 Bruhat-Tits (BT) 树几何形状的网络边界条件。我们证明了这种几何以一种独特的方式满足涌现图爱因斯坦方程，该方程与编码与张量网络相同的相关函数的体积有效物质作用一致，至少在远离纯BT 树的顺序的扰动极限顺序中。此外，数学中图曲率的（微扰）定义 [Y. 林和 S.-T。丘，东北数学。J. 63 , 605 (2011)；Y.奥利维尔，J. 功能。肛门。 256 , 810 (2009)] 和物理学 [S. S. Gubser等人。, J. 高能物理。06 ( 2017 ) 157] 文献自然而然地从涌现爱因斯坦方程的一致性要求中涌现出来。这可以为理解可能编码在更一般张量网络中的引力动力学提供新的见解。

更新日期：2021-11-23

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