More on Supersymmetric Domain Walls, N Counting and Glued Potentials

TL;DR

The paper investigates domain walls in N=1 SUSY gauge theories, focusing on N-dependence, flux tubes ending on walls, and the fate of walls in models with glued (Veneziano–Yankielowicz) potentials. It shows that cusp structures arise when heavy modes restructure across cusps, yielding missing energy contributions that must be added to naive low-energy calculations, and explains how the wall tension can scale linearly with N rather than quadratically. Through simple toy models and a supersymmetric multi-sector construction, it demonstrates the necessity of accounting for heavy-field dynamics to determine wall existence and tension, and discusses KK-domain walls and discrete anomaly matching to situate these walls in a broader nonperturbative framework. The work provides a bridge between field-theoretic domain-wall physics and D-brane intuition, clarifying when low-energy effective actions suffice and when heavy degrees of freedom dominate wall energetics.

Abstract

Various features of domain walls in supersymmetric gluodynamics are discussed. We give a simple field-theoretic interpretation of the phenomenon of strings ending on the walls recently conjectured by Witten. An explanation of this phenomenon in the framework of gauge field theory is outlined. The phenomenon is argued to be particularly natural in supersymmetric theories which support degenerate vacuum states with distinct physical properties. The issue of existence (or non-existence) of the BPS saturated walls in the theories with glued (super)potentials is addressed. The amended Veneziano-Yankielowicz effective Lagrangian belongs to this class. The physical origin of the cusp structure of the effective Lagrangian is revealed, and the limitation it imposes on the calculability of the wall tension is explained. Related problems are considered. In particular, it is shown that the so called discrete anomaly matching, when properly implemented, does not rule out the chirally symmetric phase of supersymmetric gluodynamics, contrary to recent claims.

Figures (5)

• Figure 1: The scalar potential in the model considered in Sect. 3.2.
• Figure 2: The effective potential obtained after the heavy field $\phi$ is integrated out. The cusp at $\chi =0$ reflects a restructuring of the vacua in the $\phi$ sector.
• Figure 3: A superpotential with two mountain ridges and a canyon and five vacuum states.
• Figure 4: The projection of the superpotential of Fig. 3 onto the ${\cal W}\chi$ plane. Shown are the shapes of the mountain ridges and the canyon bottom. The points of extrema in ${\cal W}$ are denoted by $A,B,C,D,E$.
• Figure 5: The two-photon matrix element of $NG\tilde{G}$. The photons are assumed to be on mass shell.