  We present the case that Luttinger liquids are characterized by a form of
hidden order which is similar, but distinct in some crucial regards, to the
hidden order characterizing spin-1 Heisenberg chains. We construct a string
correlator for the Luttinger liquid which is similar to the string correlator
constructed by den Nijs and Rommelse for the spin chain. From a geometric
prespective on the so-called `squeezed space' construction, we demonstrate that
the physics at long wavelength can be reformulated in terms of a $Z_2$ gauge
theory. Peculiarly, the normal spin chain lives at infinite gauge coupling
where it is characterized by deconfinement. We identify the microscopic
conditions required for confinement thereby identifying a novel phase of the
spin-chain. We demonstrate that the Luttinger liquid can be approached in the
same general framework. The difference from the spin chain is that the gauge
sector is critical in the sense that the Luttinger liquid is at the phase
boundary where the $Z_2$ local symmetry emerges. We evaluate the string
correlator analytically and show that the squeezed space structure is present
both for the strongly coupled Hubbard model and the non-interacting fermion
gas. These structures are hard-wired in the mathematical structure of
bosonization and this becomes obvious by considering string correlators.
Numerical results are presented for the string correlator using a non-abelian
version of the density matrix renormalization group algorithm, confirming in
detail the expectations following from the theory. We conclude with some
observations regarding the generalization of bosonization to higher dimensions.
