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 ${\tilde{G}}_{UV}$.

Comments: 11 pages, 4 figures