Baryon Number-Induced Chern-Simons Couplings of Vector and Axial-Vector Mesons in Holographic QCD

We show that holographic models of QCD predict the presence of a Chern-Simons coupling between vector and axial-vector mesons at finite baryon density. In the AdS/CFT dictionary, the coefficient of this coupling is proportional to the baryon number density, and is fixed uniquely in the five-dimensional holographic dual by anomalies in the flavor currents. For the lightest mesons, the coupling mixes transverse $\rho$ and $a_1$ polarization states. At sufficiently large baryon number densities, it produces an instability, which causes the $\rho$ and $a_1$ mesons to condense in a state breaking both rotational and translational invariance.