  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.
