Complex BPS domain walls and phase transition in mass in supersymmetric QCD

TL;DR

The paper investigates complex BPS domain walls in mass-deformed supersymmetric QCD by analyzing a two-field TVY-type effective theory and solving the BPS equations. It shows that BPS-domain-wall solutions exist only when the mass satisfies $m \le m_*$ with $m_* \approx 4.6705$, and that no such solution exists for larger $m$, indicating a mass-driven phase transition in the wall sector. The transition is not thermodynamic (vacuum energy remains zero and supersymmetry remains unbroken) but represents a qualitative change in wall spectra, with numerical diagnostics such as a mismatch parameter $\Delta(m)$ signaling the breakdown of BPS solutions. Discussing implications for large-$m$ limits and potential connections to Seiberg–Witten–like stability structures, the work suggests there is no smooth crossover between weak-coupling Higgs-like behavior and strong-coupling dynamics in this theory.

Abstract

We study the domain walls connecting different chirally asymmetric vacua in supersymmetric QCD. We show that BPS - saturated solutions exist only in the limited range of mass. When m exceeds some critical value, the domain wall either ceases to be BPS - saturated or disappears altogether. In any case, the properties of the system are qualitatively changed.

Figures (4)

• Figure 1: Mismatch parameter $\Delta$ as a function of mass
• Figure 2: $\rho(z)$ for different masses.
• Figure 3: $R(z)$ for different masses.
• Figure 4: The ratio $\eta = R(0)/R(\infty)$ as a function of mass