On the stability of Yang-Mills vacuum

Abstract

The (anti)self-dual covariantly constant vacuum fields have positive/stable and infinitely many zero modes, so called Leutwyller chromons. A regularisation method is suggested that allows to sum the contribution of the zero modes and to obtain the effective Lagrangian that has contribution of all positive/stable modes and zero modes. In the second approach we integrated over the collective coordinates of the nonlinearly interacting zero modes and obtained the same result. The last method is a generalisation of the t'Hooft integration over the instanton zero mode collective coordinates. It is important that both methods lead to the same result indicating the robustness of the logarithmic structure of the effective Lagrangian.