de Sitter symmetries and inflationary scalar-vector models

In this paper, we study the correspondence between a field theory in de Sitter space in $D$-dimensions and a dual conformal field theory in a euclidean space in $(D-1)$-dimensions. In particular, we investigate the form in which this correspondence is established for a system of interacting scalar and a vector fields propagating in de Sitter space. We analyze some necessary (but not sufficient) conditions for which conformal symmetry is preserved in the dual theory in $(D-1)$-dimensions, making possible the establishment of the correspondence. The discussion that we address on this paper is framed on the context of inflationary cosmology, so, the results obtained here pose some relevant possibilities of application to the calculation of the fields's correlation functions and of the primordial curvature perturbation $\zeta$, in inflationary models including coupled scalar and vector fields.