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 Anti de Sitter/Conformal Field Theory 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.