Patterns of chiral symmetry breaking and a candidate for a C-theorem in four dimensions

Abstract

We test a candidate for a four-dimensional C-function. This is done by considering all asymptotically free, vectorlike gauge theories with N_f flavors and fermions in arbitrary representations of any simple Lie group. Assuming spontaneous breaking of chiral symmetry in the infrared limit and that the value of the C-function in this limit is determined by the number of Goldstone bosons, we find that only in the case of a theory with two colors and fermions in one single pseudo-real representation of SU(2) the C-theorem seems to be violated. Conversely, this might also be a sign of new constraints, restricting the number of flavors consistent with spontaneous chiral symmetry breaking. For all other groups and representations we find that this candidate C-function decreases along the renormalization group flow.

RevTeX 5 pages

References in corpus (3)

• Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature
• Exact Consequences of the Trace Anomaly in Four Dimensions
• The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories

Cited by in corpus (1)

• Can Renormalization Group Flow End in a Big Mess?