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Essential to understanding the cuprate pseudogap phase is a study of thecharge (and spin) response functions, which we address here via a consistentapproach to the Fermi arcs and the Fermi pockets scenario of Yang, Rice andZhang (YRZ). The two schemes are demonstrated to be formally similar, and toshare a common physics platform; we use this consolidation to address theinclusion of vertex corrections which have been omitted in YRZ applications. Weshow vertex corrections can be easily implemented in a fashion analyticallyconsistent with sum rules and that they yield important contributions to mostobservables. A study of the charge ordering susceptibility of the YRZ scenariomakes their simple physics evident: they represent the inclusion of chargedbosonic, spin singlet degrees of freedom, and are found to lead to a doublepeak structure.

Unified treatment of Fermi pockets and arcs scenarios for the cuprates: Sum rule consistent response functions of the pseudogap