Axial anomalies in gauge theory by exact renormalization group method

Abstract

The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff $Ł$ and the boundary conditions for the relevant couplings. The physical theory is obtained at $Ł=0$. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point $Ł=Ł_0\to\infty$ but at the physical value $Ł=0$. As an illustration, we compute the triangle axial anomalies.