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 pseudoreal representation of SU(2) does the C theorem seem 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.

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