RG generated fermion mass

Abstract

Chiral symmetry breaking in a purely fermionic theory is investigated by the help of the renormalization group method. The RG equation for the running mass $m_k$ admits a solution with vanishing bare mass and finite physical mass. The running Fermi coupling constant, $G_k$, converges to a finite (renormalized) physical value. It is also shown that the RG equation for $\tilde G$, the dimensionless Fermi coupling, has an UV fixed point $\tilde G_{UV}$. Contrary to a previous result however, it is proven that the chiral symmetry breaking point $\tilde G_c$ does not coincide with $\tilde G_{UV}$.