  We construct a new vacuum for loop quantum gravity, which is dual to the
Ashtekar-Lewandowski vacuum. Because it is based on BF theory, this new vacuum
is physical for $(2+1)$-dimensional gravity, and much closer to the spirit of
spin foam quantization in general. To construct this new vacuum and the
associated representation of quantum observables, we introduce a modified
holonomy-flux algebra which is cylindrically consistent with respect to the
notion of refinement by time evolution suggested in [1]. This supports the
proposal for a construction of a physical vacuum made in [1,2], also for
$(3+1)$-dimensional gravity. We expect that the vacuum introduced here will
facilitate the extraction of large scale physics and cosmological predictions
from loop quantum gravity.
