Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
High Energy Physics - Theory
2018-06-13 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Quantum Physics
Abstract
We consider the special case of Random Tensor Networks (RTN) endowed with gauge symmetry constraints on each tensor. We compute the R\`enyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background independent quantum gravity, and for importing quantum gravity tools in tensor network research.
Keywords
Cite
@article{arxiv.1711.09941,
title = {Ryu-Takayanagi Formula for Symmetric Random Tensor Networks},
author = {Goffredo Chirco and Daniele Oriti and Mingyi Zhang},
journal= {arXiv preprint arXiv:1711.09941},
year = {2018}
}
Comments
10 pages, 4 figures