# The Large $N$ Limit of icMERA and Holography

### Submission summary

 As Contributors: Javier Molina Vilaplana Arxiv Link: https://arxiv.org/abs/2107.13248v2 (pdf) Date submitted: 2021-09-22 09:30 Submitted by: Molina Vilaplana, Javier Submitted to: SciPost Physics Academic field: Physics Specialties: Gravitation, Cosmology and Astroparticle Physics High-Energy Physics - Theory Quantum Physics Approach: Theoretical

### Abstract

In this work we compute the entanglement entropy in continuous icMERA tensor networks for large $N$ models at strong coupling. Our results show that the $1/N$ quantum corrections to the Fisher information metric (interpreted as a local bond dimension of the tensor network) in an icMERA circuit, can be related to quantum corrections to the minimal area surface in the the Ryu-Takayanagi formula. Upon picking two different non-Gaussian entanglers to build the icMERA circuit, the results for the entanglement entropy only differ at subleading orders in $1/G_N$, i.e., at the structure of the quantum corrections in the bulk. The fact that the large $N$ part of the entropy can be always related to the leading area term of the holographic calculation results thus very suggestive. These results, which to our knowledge suppose the first tensor network calculations at large $N$ and strong coupling, pave the road for using tensor networks to describe the emergence of continuous spacetime geometries from the the structure of entanglement in quantum field theory.

###### Current status:
Editor-in-charge assigned