Spin-1 Glueballs in the Witten-Sakai-Sugimoto Model

We consider the vector and the pseudovector glueball in the top-down holographic model of large-$N_c$ QCD of Witten and their decays into ordinary mesons described by the D8 brane construction due to Sakai and Sugimoto. At leading order, the relevant interactions are determined exclusively by the Chern-Simons action of the D8 branes and are thus rigidly connected to the chiral anomaly and the Wess-Zumino-Witten terms. As found in a previous study of the pseudovector glueball, which we revisit and complete, the resulting decay widths are surprisingly large, implying that both the pseudovector and the vector glueball are very broad resonances, with a conspicuous dominance of decays into $a_1\rho$ and $K_1(1400) K^*$ in the case of the vector glueball. We also obtain a certain weak mixing of vector glueballs with ordinary vector mesons, but we conclude that it does not provide an explanation for the so-called $\rho\pi$ puzzle in charmonium decays.