The phase structure of Einstein-Cartan theory

TL;DR

This paper investigates the phase structure of Einstein-Cartan gravity coupled to fermions, identifying three distinct phases based on four-fermion interaction strength and analyzing phase transitions and effective low-energy theories.

Contribution

It provides a detailed analysis of the phase diagram and critical points in Einstein-Cartan theory with fermions, revealing new phases and transition behaviors.

Findings

Identified three distinct fermion phases based on interaction strength.

Determined critical points for phase transitions between phases.

Discussed the low-energy effective theory in the scaling-invariant region.

Abstract

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}.