APD-Invariant Tensor Networks from Matrix Quantum Mechanics

TL;DR

This paper introduces a novel tensor network framework inspired by matrix quantum mechanics, featuring dynamic geometry, background independence, and emergent gauge fields, potentially modeling sub-AdS physics.

Contribution

It establishes a connection between matrix quantum mechanics and tensor networks, enabling background-independent, $U(N)$ invariant states with emergent gauge fields and string-like nonlocality.

Findings

Tensor networks with dynamically determined geometry.

Emergence of $U(p)$ gauge fields on network links.

Potential modeling of sub-AdS physics with string-scale nonlocality.

Abstract

We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is determined dynamically, giving a notion of background independence. The tensor network states have a $U(N)$ invariance, which (a) allows us to consider continuous families of entanglement cuts even with a finite number of tensors and (b) includes a notion of bulk coordinate reparameterization and area-preserving diffeomorphism invariance in the large N limit. These tensor networks also have a natural scale of nonlocality that behaves similarly to a string scale, suggesting a potential toy model for sub-AdS physics. Emergent $U(p)$ gauge fields naturally appear on the tensor network links.