Theta dependence in Holographic QCD

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.