  The conductivity properties between Luttinger liquids are analyzed by exact
Renormalization Group methods. We prove that in a two chain system or in a
model of bilayer graphene, described by two coupled fermionic honeycomb
lattices interacting with a gauge field, the transverse optical conductivity at
finite temperature is anomalous and decreasing together with the frequency as a
power law with Luttinger liquid exponent.
