  Our current understanding of strongly correlated electron systems is based on
a homogeneous framework. Here we take a step going beyond this paradigm by
incorporating inhomogeneity from the beginning. Specifying to systems near the
Mott metal-insulator transition, we propose a real space picture of itinerant
electrons functioning in the fluctuating geometries bounded by interfaces
between metallic and insulating regions. In 2+1-dimensions, the interfaces are
closed bosonic strings, and we have a system of strings coupled to itinerant
electrons. When the interface tension vanishes, the geometric fluctuations
become critical, which gives rise to non-Fermi liquid behavior for the
itinerant electrons. In particular, the poles of the fermion Green's function
can be converted to zeros, indicating the absence of propagating
quasiparticles. Furthermore, the quantum geometric fluctuations mediate Cooper
pairing among the itinerant electrons, indicating the intrinsic instability of
electronic systems near the Mott transition.
