We extend Witten's result that dynamical supersymmetry breaking does not occur in non-Abelian gauge theories which do not depend on a vacuum angle. It is shown that the possibility of dynamical supersymmetry breaking in supersymmetric non-Abelian gauge theories is intimately related to the asymptotic freedom of Yang-Mills theories. In supersymmetric non-Abelian gauge theories with asymptotic freedom, dynamical supersymmetry breaking does not occur through a positive vacuum energy for an arbitrary gauge coupling constant regardless of any dependence on the vacuum angle in the theories, assuming the full gauge symmetry in the limit of small $g$ in the quantum theory. Such a special example is the minimal supersymmetric non-Abelian gauge theories in four dimensions.

• Received 6 September 1991

DOI:https://doi.org/10.1103/PhysRevD.45.2165