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We test a candidate for a four-dimensional C-function. This is done byconsidering all asymptotically free, vectorlike gauge theories with N_f flavorsand fermions in arbitrary representations of any simple Lie group. Assumingspontaneous breaking of chiral symmetry in the infrared limit and that thevalue of the C-function in this limit is determined by the number of Goldstonebosons, we find that only in the case of a theory with two colors and fermionsin one single pseudo-real representation of SU(2) the C-theorem seems to beviolated. Conversely, this might also be a sign of new constraints, restrictingthe number of flavors consistent with spontaneous chiral symmetry breaking. Forall other groups and representations we find that this candidate C-functiondecreases along the renormalization group flow.Comment: RevTeX 5 page

Patterns of chiral symmetry breaking and a candidate for aCtheorem in four dimensions