Gauge Freedom in Chiral Gauge Theory with Vacuum Overlap – Four-dimensional case

Dynamical nature of the gauge degree of freedom and its effect to fermion spectrum are studied for four-dimensional nonabelian chiral gauge theory in the vacuum overlap formulation. The covariant gauge fixing term and the Faddeev-Popov determinant are introduced by hand as a weight for the gauge average. At β = ∞, as noticed by Hata some time ago, the model is renormalizable at one-loop and the gauge fixing term turns into an asymptotically free self-coupling of the gauge freedom, even in the presence of the gauge symmetry breaking of the complex phase of chiral determinant. The severe infrared divergence occurs in the perturbation expansion and it prevents local order parameters from emerging. The Foerster-Nielsen-Ninomiya mechanism works in this perturbative framework: the small explicit gauge symmetry breaking term does not affect the above infrared structure. Based on these dynamical features, which is quite similar to the two-dimensional nonlinear sigma model, we assume that the global gauge symmetry does not break spontaneously and the gauge freedom acquires mass dynamically. The asymptotic freedom allows us to tame the gauge fluctuation by approaching the critical point of the gauge freedom without spoiling its disordered nature. Then it is argued that the disordered gauge freedom does not necessarily cause the massless chiral state in the (waveguide) boundary correlation function and that the entire fermion spectrum can be chiral. e-mail address: [email protected], [email protected] On leave of absence from: Department of Physics, Kyoto University, Kyoto 606-01, Japan 1