Domain Walls in Supersymmetric Yang-Mills Theories
A. Kovner, M. Shifman, A. Smilga
TL;DR
This paper shows that domain walls in supersymmetric Yang–Mills theories and their SQCD extensions are robust, BPS-saturated objects whose tensions are fixed by a central charge and holomorphic dynamics, as captured by corrected Veneziano–Yankielowicz Lagrangians. It provides explicit wall profiles and exact energy densities, demonstrates smooth coupling transitions via holomorphy, and analyzes wall behavior across mass deformations, including Higgs-phase walls and the decay of false vacua under soft SUSY breaking. It also addresses the toron controversy, arguing that in the large-volume limit the topological charge is effectively integer and domain walls persist. The work yields exact, testable relations between scale parameters, wall tensions, and condensates, with implications for the nonperturbative structure of SUSY gauge theories.
Abstract
We present a detailed analysis of the domain walls in supersymmetric gluodynamics and SQCD. We use the (corrected) Veneziano-Yankielowicz effective Lagrangians to explicitely obtain the wall profiles and check recent results of Dvali and Shifman (Phys. Lett. B396, (1997) 64: (i) the BPS-saturated nature of the walls; (ii) the exact expressions for the wall energy density which depend only on global features of dynamics (the existence of a non-trivial 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 SU(N) SUSY gluodynamics.