Holography for Small Values of the Cosmological Constant

TL;DR

This paper reviews recent advances in holography for finite area causal diamonds, focusing on their description within the AdS/CFT correspondence and introducing a novel tensor network approach.

Contribution

It presents a new tensor network construction that maintains rotation invariance and clarifies the operator algebra in finite area causal diamonds within holography.

Findings

Operator algebra in finite area diamonds is well-defined with a UV cutoff tensor network.

The tensor network construction preserves rotation invariance.

No simple relation exists between finite diamond operator algebra and boundary von Neumann algebras.

Abstract

We review recent work on holography for finite area causal diamonds and explore its implications for the description of such diamonds in the Anti-deSitter space Conformal Field Theory correspondence. We argue that the algebra of operators in a finite area diamond is well defined in a UV cutoff tensor network construction, but is not related in any simple way to any infinite von Neumann sub-algebra of the boundary algebra or its cross product. Our argument relies on a novel construction of tensor networks that preserves rotation invariance.