  We present a fractionalized metallic phase which is indistinguishable from
the Fermi liquid in conductivity and thermodynamics, but is sharply distinct in
one electron properties, such as the electron spectral function. We dub this
phase the `Orthogonal Metal.' The Orthogonal Metal and the transition to it
from the Fermi liquid are naturally described using a slave particle
representation wherein the electron is expressed as a product of a fermion and
a slave Ising spin. We emphasize that when the slave spins are disordered the
result is not a Mott insulator (as erroneously assumed in the prior literature)
but rather the Orthogonal Metal. We construct prototypical ground state
wavefunctions for the Orthogonal Metal by modifying the Jastrow factor of
Slater-Jastrow wavefunctions that describe ordinary Fermi liquids. We further
demonstrate that the transition from the Fermi liquid to the Orthogonal Metal
can, in some circumstances, provide a simple example of a continuous
destruction of a Fermi surface with a critical Fermi surface appearing right at
the critical point. We present exactly soluble models that realize an
Orthogonal Metal phase, and the phase transition to the Fermi liquid. These
models thus provide valuable solvable examples for phase transitions associated
with the death of a Fermi surface.
