  It has been believed that the superinsulating state which is the
low-temperature charge Berezinskii-Kosterlitz- Thouless (BKT) phase can exist
only in two dimensions. We develop a general gauge description of the su-
perinsulating state and the related deconfinement transition of Cooper pairs
and predict the existence of the superinsulating state in three dimensions
(3d). We find that 3d superinsulators exhibit Vogel-Fulcher-Tammann (VFT)
critical behavior at the phase transition. This is the 3d string analogue of
the Berezinski-Kosterlitz- Thouless (BKT) criticality for logarithmically and
linearly interacting point particles in 2d. Our results show that singular
exponential scaling behaviors of the BKT type are generic for phase transitions
associated with the condensation of topological excitations.
