Jackiw-Johnson sum rule for dynamical symmetry breaking

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Abstract
We reconsider the Jackiw-Johnson sum rule relating the vector-boson masses (or Goldstone-boson decay constants) to the interactions of the fermions which condense. We show that the counterterm can be simplified to remove all reference to chiral-symmetry breaking, producing a much simpler formula involving no derivatives of the fermion self-energy. This is useful for applications to QCD and technicolor. In the process, we also generalize the sum rule to the breaking of an arbitrary symmetry group, paying particular attention to the requirements of gauge invariance and current conservation.