Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD

TL;DR

The paper analyzes the worldvolume dynamics of 1/2-BPS domain walls in ${\cal N}=1$ SQCD with $N_f=N$, revealing an enhancement of supersymmetry on the reduced moduli space ${\widetilde{\cal M}}$ when this space has a Kahler structure. It explicitly constructs the worldvolume algebra, showing the effective theory on the wall is a ${\cal N}=2$ Kahler sigma-model deformed by a real-mass potential, and demonstrates this framework describes novel 1/4-BPS two-wall junctions as kinks on the wall with two preserved worldvolume supercharges. In the SU(2) case, equal masses yield a ${\mathbb{C}}P^1$ worldvolume with two vacua, while a mass split introduces a Killing-vector potential that preserves ${\cal N}=2$ SUSY. The analysis extends to general ${\rm SU}(N)$, where junction multiplicities follow the CFIV index and tensions exhibit a sine-law form protected by enhanced worldvolume SUSY, linking bulk soliton spectra to exactly solvable worldvolume dynamics. These results illuminate non-perturbative soliton behavior and suggest broader applicability to similar SUSY theories and brane-inspired pictures.

Abstract

We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an N=2 Kahler sigma model in 2+1D deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall junction configurations, which are 1/4-BPS objects, but nonetheless preserve two supercharges when viewed as kinks on the wall worldvolume.

Figures (3)

• Figure 1: A schematic representation of the $N$ vacua, and a $k$-wall, for ${\cal N}\!\!=\!1\;$ SQCD with $N$ flavors.
• Figure 2: A schematic representation of a 'boosted' BPS junction, i.e. a junction superposed with a wave of momentum $P_3$.
• Figure 3: The wall junction geometry, indicating the field profiles in the $W_+$ and $W_-$ components. Note that, by continuity, the fields near the junction must pass through the strong-coupling regions near $Y=0$, where the low energy description breaks down.