A note on the architecture of spacetime geometry

Understand

Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra.

• We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure naturally leads to the Bekenstein-Hawking formula of the entanglement entropy for any macroscopic spacetime region.
• This suggests that a smooth spacetime geometry could be recovered in such a way, as conjectured by Bianchi and Myers.
• Some comparison with Xiao-Gang Wen's string-net picture of gauge theory is made.