The Universe As A Holographic Quasicrystalline Tensor Network

ncatlab |  The AdS-CFT correspondence at its heart is the observation (Witten 98, Section 2.4) that the classical action functionals for various fields coupled to Einstein gravity on anti de Sitter spacetime are, when expressed as functions of the asymptotic boundary-values of the fields, of the form of generating functions for correlators/n-point functions of a conformal field theory on that asymptotic boundary, in a large N limit.

This is traditionally interpreted as a concrete realization of a vague “holographic principle” according to which quantum gravity in bulk spacetimes is controlled, in one way or other, by “boundary field theories” on effective spacetime boundaries, such as event horizons. The original and main motivation for the holographic principle itself was the fact that the apparent black hole entropy in Einstein gravity scales with the area of the event horizon instead of the black hole’s bulk volume (which is not even well-defined), suggesting that gravity encodes or is encoded by some boundary field theory associated with horizons; an idea that, in turn, seems to find a concrete realization in open/closed string duality in the vicinity of, more generally, black branes. The original intuition about holographic black hole entropy has meanwhile found remarkably detailed reflection in (mathematically fairly rigorous) analysis of holographic entanglement entropy, specifically via holographic tensor networks, which turn out to embody key principles of the AdS/CFT correspondence in the guise of quantum information theory, with concrete applications such as to quantum error correcting codes.

quantumgravityresearch |  Recent advances in AdS/CFT holography have found an analogue in discrete tensor networks of qubits. The {5,4} hyperbolic tiling allows for topological error correction. We review a simple 32 x 32 Hamiltonian from five maximally entangled physical qubits on the boundary edges of a pentagon, whose two-fold degenerate ground state leads to an emergent logical qubit in the bulk. The inflation rule of a holographic conformal quasicrystal is found to encode the holographic code rate that determines the ratio of logical qubits to physical qubits. Generalizing SU(2) qubits to twistors as conformal spinors of SU(2,2), an H3-symmetric 5-compound of cuboctahedral A3 = D3 root polytopes is outlined. Motivated by error correction in the Hamming code, the E8 lattice is projected to the H4-symmetric quasicrystal. The 4-dimensional 600-cell is found to contain five 24-cells associated with the D4 root polytope associated with Spin(4,4). Intersection with Sp(8,R) phase space identifies three generations of conformal symmetry with an axial U(1) symmetry. A lightning review of E8(-24) phenomenology with Spin(12,4) is pursued for gravity and the standard model with a notion of CDT-inspired discretized membranes in mind. Warm dark matter beyond the standard model is briefly articulated to stem from intersecting worldvolumes related to the Leech lattice associated with the Golay code, hinting at a monstrously supersymmetric M-theory in D=26+1. A new D=27+3 superalgebra is shown to contain membranes that can give a worldvolume description of M-theory and F-theory.