Correlation functions of sourced gravitational waves in inflationary
  scalar vector models. A symmetry based approach
  We use conformal symmetry to constrain the shape of inflationary correlators
in the presence of long-lived vector field perturbations. Applying conformal
Ward identities, we derive general expressions, up to amplitudes and
normalization factors, for the two and three point correlators in the presence
of 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 a
suitable coupling function between the scalar and the vector field. The
previous interaction allows for isotropy and parity symmetry breaking and is
consistent with super horizon conformal symmetry. As an application of the
conformal field theory techniques followed here, we evaluate the mixed
tensor-scalar $\langle \gamma \zeta \rangle$ and tensor-scalar-scalar $\langle
\gamma \zeta \zeta \rangle$ correlators which are interesting to look for
parity violating effects related with chiral gravitational waves. Finally, we
derive consistency relations for the three point correlators obtained.
