Domain walls in supersymmetric Yang-Mills theories

We present a detailed analysis of the domain walls in supersymmetric gluodynamics and SQCD. We use the (corrected) Veneziano-Yankielowicz effective Lagrangians to explicitly obtain the wall profiles and check recent results of Dvali and Shifman: (i) the BPS-saturated nature of the walls and (ii) the exact expressions for the wall energy density which depend only on global features of dynamics (the existence of a nontrivial central extension of $N=1$ superalgebra in the theories which admit wall-like solutions). If supersymmetry is softly broken by the gluino mass, the degeneracy of the distinct vacua is gone, and one can consider the decay rate of the ``false'' vacuum into the genuine one. We do this calculation in the limit of the small gluino mass. Finally, we comment on the controversy regarding the existence of $N$ distinct chirally asymmetric vacua in $\mathrm{SU}(N)$ SUSY gluodynamics.