  We compare the pole structure of the electronic Green's function obtained by
Cluster Dynamical Mean Field Theory to the results from the fractionalized Pair
Density Wave idea. In the superconducting phase, we can consider the system in
a state with coexistence of Superconducting and Charge order. Writing the
Green's function in a way analogous to the previously proposed
"hidden-fermions" model from S. Sakai et al (2016) leads to a similar pole
structure for the self-energy. The fractionalization of the Pair Density Wave
order also describes the pseudogap phase as a superposition of superconducting
and charge order fluctuations. Considering a phenomenological lifetime for the
particle-particle and particle-hole pairs leads to an electronic spectral
function that matches the numerical results.
