Baryons and the Chern-Simons term in holographic QCD with three flavors

We study dynamical baryons in the holographic QCD model of Sakai and Sugimoto in the case of three flavors, with special interest in the construction of the Chern-Simons (CS) term. The baryon classical solution in this model is given by the BPST instanton, and we carry out the collective coordinate quantization of this solution. The CS term should give rise to a first-class constraint which selects baryon states with the correct spins. However, the original CS term written in terms of the CS 5-form does not do so. Considering this fact, we propose a new CS term that is gauge invariant and takes the form of an integral over a six-dimensional space whose boundary is the original five-dimensional spacetime of the holographic model. Collective coordinate quantization using our new CS term leads to the correct baryon states and their mass formula.