Theta dependence in Holographic QCD

TL;DR

This paper investigates the effects of the CP-violating theta-term in holographic QCD, analyzing its impact on meson and baryon properties, and calculating related observables like the neutron electric dipole moment and pion-nucleon coupling.

Contribution

It provides a holographic analysis of theta dependence in large N_c QCD, including baryonic solutions and CP-violating observables, with results consistent with effective field theory expectations.

Findings

Baryon spectrum remains unaffected at leading order in theta.

Electromagnetic form factors exhibit vector-meson dominated dipole terms.

Neutron electric dipole moment is of the same order as previous estimates.

Abstract

We study the effects of the CP-breaking topological $\theta$-term in the large $N_c$ QCD model by Witten, Sakai and Sugimoto with $N_f$ degenerate light flavors. We first compute the ground state energy density, the topological susceptibility and the masses of the lowest lying mesons, finding agreement with expectations from the QCD chiral effective action. Then, focusing on the $N_f=2$ case, we consider the baryonic sector and determine, to leading order in the small $\theta$ regime, the related holographic instantonic soliton solutions. We find that while the baryon spectrum does not receive ${\cal O}(\theta)$ corrections, this is not the case for observables like the electromagnetic form factor of the nucleons. In particular, it exhibits a dipole term, which turns out to be vector-meson dominated. The resulting neutron electric dipole moment, which is exactly the opposite as that of the proton, is of the same order of magnitude of previous estimates in the literature. Finally, we compute the CP-violating pion-nucleon coupling constant ${\bar g}_{\pi N N}$, finding that it is zero to leading order in the large $N_c$ limit.