Domain walls and the decay rate of the excited vacua in largeNYang-Mills theory

Abstract

In the (nonsupersymmetric) Yang-Mills theory in the large $N$ limit, there exists an infinite set of nondegenerate ``vacua.'' The distinct vacua are separated by domain walls whose tension determines the decay rate of the false vacua. I discuss the phenomenon from a field-theoretic point of view, starting from supersymmetric gluodynamics and then breaking supersymmetry by introducing a gluino mass. By combining previously known results, the decay rate of the excited vacua is estimated, $\ensuremath{\Gamma}\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}\mathrm{const}\ifmmode\times\else\texttimes\fi{}{N}^{4}).$ The fourth power of $N$ in the exponent is a consequence of the fact that the wall tension is proportional to $N.$