Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-29
Phys.Lett.B665:54-57,2008
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, the 2nd Stueckelberg workshop on relativistic field theories. the version to appear in Phys. Lett. B
Scientific paper
10.1016/j.physletb.2008.05.051
In the Einstein-Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the {\it low-energy limit}.
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