  We consider the role of the Ward identity in dealing with the transport
properties of an interacting system forming a d-wave modulated charge-density
wave or staggered flux phase. In particular, we address this issue from the
point of view of the restricted optical-conductivity sum rule. Our aim is to
provide a controlled approximation for the current-current correlation function
which allows us also to determine analytically the corresponding sum rule. By
analyzing the role of the vertex functions in both the microscopic interacting
model and in the effective mean-field Hamiltonian, we propose a non-standard
low-energy sum-rule for this system. We also discuss the possible applicability
of these results for the description of cuprate superconductors in the
pseudogap regime.
