Holography for Small Values of the Cosmological Constant

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.