The CP-odd sector and $θ$ dynamics in holographic QCD

Abstract

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 $θ$ 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 $θ$ 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 $θ$-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.

58 pages plus appendices, 19 figures. V2: section 3.1 improved, typos corrected, published version