  The holographic model of V-QCD is used to analyze the physics of QCD in the
Veneziano large-N limit. An unprecedented analysis of the CP-odd physics is
performed going beyond the level of effective field theories. The structure of
holographic saddle-points at finite $\theta$ is determined, as well as its
interplay with chiral symmetry breaking. Many observables (vacuum energy and
higher-order susceptibilities, singlet and non-singlet masses and mixings) are
computed as functions of $\theta$ and the quark mass $m$. Wherever applicable
the results are compared to those of chiral Lagrangians, finding agreement. In
particular, we recover the Witten-Veneziano formula in the small $x\to 0$
limit, we compute the $\theta$-dependence of the pion mass and we derive the
hyperscaling relation for the topological susceptibility in the conformal
window in terms of the quark mass.
