Domain walls and theta dependence in QCD with an effective Lagrangian approach

We suggest an anomalous effective Lagrangian which reproduces the anomalous conformal and chiral Ward identities and topological charge quantization in QCD. It is shown that the large N_c Di Vecchia–Veneziano–Witten effective chiral Lagrangian is locally recovered from our results, along with 1/N_c corrections, after integrating out the heavy “glueball” fields. All dimensionful parameters in our scheme are fixed in terms of the quark and gluon condensates and quark masses. We argue that for a certain range of parameters, metastable vacua appear which are separated from the true vacuum of lowest energy by domain walls. The surface tension of the wall is estimated, and the dynamics of the wall is discussed. The U(1) problem and the physics of the pseudo Goldstone bosons at different θ angles are addressed within the effective Lagrangian approach. Implications for axion physics, heavy ion collisions and the development of the early Universe during the QCD epoch are discussed.