The CP-odd sector and $\theta$ dynamics in holographic QCD

TL;DR

This paper uses a holographic V-QCD model to analyze CP-odd phenomena in QCD, exploring the effects of the theta parameter on various observables and comparing results with chiral Lagrangians, including the Witten-Veneziano formula.

Contribution

It provides a detailed holographic analysis of CP-odd physics in QCD, extending beyond effective field theories and computing multiple observables as functions of theta and quark mass.

Findings

Recovered the Witten-Veneziano formula in the small x limit

Computed theta dependence of pion mass

Derived hyperscaling relation for topological susceptibility

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 $\theta$ 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.