  An intense investigation of possible non-Fermi liquid states of matter has
been inspired by two of the most intriguing phenomena discovered in the past
quarter century, namely high temperature superconductivity and the fractional
quantum Hall effect. Despite enormous conceptual strides, these two fields have
developed largely along separate paths. Two widely employed theories are the
resonating valence bond theory for high temperature superconductivity and the
composite fermion theory for the fractional quantum Hall effect. The goal of
this "perspective" article is to note that they subscribe to a common
underlying paradigm: they both connect these exotic quantum liquids to certain
ordinary Fermi liquids residing in unphysical Hilbert spaces. Such a relation
yields numerous nontrivial experimental consequences, exposing these theories
to rigorous and definitive tests.
