Dynamical breaking of supersymmetry and positivity of vacuum energy density

The possibility of dynamical breaking of supersymmetry is investigated with special emphasis on the role of the positivity of the vacuum energy density. We point out that (i) the vacuum energy density can become negative after appropriate renormalization of the fields (thereby being energetically favorable over the supersymmetric case), yet (ii) in such a situation the Nambu-Goldstone fermion state must necessarily possess negative norm, the theory becoming physically unacceptable. This phenomenon is explicitly demonstrated using an O(N) symmetric Wess-Zumino type model in the large-N limit. We conclude that for dynamical breaking of supersymmetry to occur in a physically acceptable manner, it is necessary that supersymmetric solution(s) be completely destroyed. Our study suggests that a strong power-type infrared singularity might achieve such a situation.