Anomalous mass dimensions and Schwinger–Dyson equations boundary condition

Abstract

Theories with large mass anomalous dimensions (γm) have been extensively studied because of their deep consequences for models where the scalar bosons are composite. Large γm values may appear when a non-Abelian gauge theory has a large number of fermions or is affected by four-fermion interactions. In this note we provide a simple explanation how γm can be directly read out from the IR and UV boundary conditions derived from the gap equation, and verify that moderate γm values appear when the theory possess a large number of fermions, but large γm values are obtained only when four-fermion interactions are added to the theory. We also verify how the critical line separating the different chiral phases emerge from these conditions.