This talk is a re-recording of a talk given by David Chester to Louis Kauffman’s Quantum Topology seminary at the University of Illinois at Chicago on March 24th, 2022.
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.
