Fractionalizing a local pair density wave: a good "recipe" for opening a pseudo-gap

We give a concise version of a recently proposed concept of fractionalization of an order parameter, thus generating a constraint through a fictitious gauge field. We argue that this new line of approach is key to explain the longstanding mystery of the pseudo-gap phase in cuprate superconductors. For example, the fractionalization of a finite momentum, charge two state living on latice bonds -- also called Pair Density Wave, into a particle-particle and a particle-hole pair leads to the opening of a gap in the fermionic spectrum. It induces "phase-locking" between the particle-particle and particle-hole pairs. We describe the formation of the Fermi arcs in the spectrum and give an account of recent Raman spectroscopy results from a minimal microscopic model. We relate the "phase-locking" to intriguing STM experimental observations.