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Insulating quantum spin liquids can undergo a confinement transition to avalence bond solid state via the condensation of topological excitations of theassociated gauge theory. We extend the theory of such transitions tofractionalized Fermi liquids (FL*): these are metallic doped spin liquids inwhich the Fermi surfaces only have gauge neutral quasiparticles. Using insightsfrom a duality transform on a doped quantum dimer model for the U(1)-FL* state,we show that projective symmetry group of the theory of the topologicalexcitations remains unmodified, but the Fermi surfaces can lead to additionalfrustrating interactions. We propose a theory for the confinement transition of$\mathbb{Z}_2$-FL* states via the condensation of visons. A variety ofconfining, incommensurate density wave states are possible, including some thatare similar to the incommensurate $d$-form factor density wave order observedin several recent experiments on the cuprate superconductors.

Confinement transition to density wave order in metallic doped spin liquids