Bidirectional holographic codes and sub-AdS locality

TL;DR

This paper introduces advanced tensor network models that better capture key features of holographic duality, including bulk-boundary correspondence, gauge symmetry, and emergent locality, addressing limitations of previous toy models.

Contribution

It proposes a new class of tensor network models that incorporate holographic interpretation, bulk gauge symmetry, and sub-AdS geometry, improving upon earlier models of holographic duality.

Findings

Models reproduce Ryu-Takayanagi entropy formula

Bulk operators can be redundantly mapped to boundary

Emergent bulk locality for sparse excitations

Abstract

Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce the Ryu-Takayanagi entropy formula for boundary intervals, and allow bulk operators to be mapped to the boundary in a redundant fashion. These exactly solvable, explicit models have provided valuable insight but nonetheless suffer from many deficiencies, some of which we attempt to address in this article. We propose a new class of tensor network models that subsume the earlier advances and, in addition, incorporate additional features of holographic duality, including: (1) a holographic interpretation of all boundary states, not just those in a "code" subspace, (2) a set of bulk states playing the role of "classical geometries" which reproduce the Ryu-Takayanagi formula for boundary intervals, (3) a bulk gauge symmetry analogous to diffeomorphism invariance in gravitational theories, (4) emergent bulk locality for sufficiently sparse excitations, and (5) the ability to describe geometry at sub-AdS resolutions or even flat space.