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We use conformal symmetry to constrain the shape of inflationary correlatorsin the presence of long-lived vector field perturbations. Applying conformalWard identities, we derive general expressions, up to amplitudes andnormalization factors, for the two and three point correlators in the presenceof vector fields mediated by the interaction $f(\phi)\left(F_{\mu \nu}F^{\mu\nu}+\alpha\tilde{F}_{\mu \nu}F^{\mu \nu}\right)$, where $f(\phi)$ is asuitable coupling function between the scalar and the vector field. Theprevious interaction allows for isotropy and parity symmetry breaking and isconsistent with super horizon conformal symmetry. As an application of theconformal field theory techniques followed here, we evaluate the mixedtensor-scalar $\langle \gamma \zeta \rangle$ and tensor-scalar-scalar $\langle\gamma \zeta \zeta \rangle$ correlators which are interesting to look forparity violating effects related with chiral gravitational waves. Finally, wederive consistency relations for the three point correlators obtained.

Correlation functions of sourced gravitational waves in inflationary scalar vector models. A symmetry based approach