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Non-Abelian topological order with SO(5) chiral edge states
We consider a chiral spin liquid constructed using the parton theory. This
state supports non-Abelian anyons and neutral fermions, which share some
similarities with the celebrated Moore-Read state. The edge physics of the
parton state and the Moore-Read state is very different. Based on conformal
field theory (CFT) analysis, it is proposed that the edge states exhibit an
emergent SO(5) symmetry. The counting of edge states in the low-lying
SO(5) CFT towers is computed. The chiral spin liquid is generated using
tensor network methods, which allows us to confirm the SO(5) counting
using entanglement spectrum. An additional feature of multiple branches in the
entanglement spectrum is observed and analyzed
Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
Between Snyder's quantized space-time model in de Sitter space of momenta and
the \dS special relativity on \dS-spacetime of radius with Beltrami
coordinates, there is a one-to-one dual correspondence supported by a minimum
uncertainty-like argument. Together with Planck length , should be a fundamental constant. They lead to a
dimensionless constant . These indicate that physics at these two scales should be dual to
each other and there is in-between gravity of local \dS-invariance
characterized by . A simple model of \dS-gravity with a gauge-like action on
umbilical manifolds may show these characters. It can pass the observation
tests and support the duality.Comment: 32 page
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