  We consider the relationship between fluid models of an interacting dark
sector, and the field theoretical models that underlie such descriptions. This
question is particularly important in light of suggestions that such
interactions may help alleviate a number of current tensions between different
cosmological datasets. We construct consistent field theory models for an
interacting dark sector that behave exactly like the coupled fluid ones, even
at the level of linear perturbations, and can be trusted deep in the nonlinear
regime. As a specific example, we focus on the case of a Dirac, Born-Infeld
(DBI) field conformally coupled to a quintessence field. We show that the fluid
linear regime breaks before the field gradients become large; this means that
the field theory is valid inside a large region of the fluid nonlinear regime.
