  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.
