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Domain Wall Junctions are 1/4-BPS States

Sean M. Carroll, Simeon Hellerman, Mark Trodden

TL;DR

This work shows that $N=1$ theories with multiple vacua admit $1/4$-BPS domain wall junctions preserving a single Hermitian supercharge, and derives both local and integral BPS bounds that constrain wall networks. It develops a long-distance, contour-based formulation of the BPS conditions and provides explicit constructions in the $Z_3$ and $Z_4$ models, including a closed-form $W(z,ar z)$ for a four-wall junction and a real, positive-definite Kähler metric realization. The analysis connects to the confining phase of $N=1$ SYM and to M-theory dual descriptions, predicting junction states in SYM and offering concrete holographic avenues via brane intersections. Overall, the paper establishes a robust framework for analyzing and constructing 1/4-BPS wall junctions, linking field-theoretic solitons to geometric and duality-inspired pictures with potential experimental relevance in nonperturbative SUSY dynamics.

Abstract

We study N=1 SUSY theories in four dimensions with multiple discrete vacua, which admit solitonic solutions describing segments of domain walls meeting at one-dimensional junctions. We show that there exist solutions preserving one quarter of the underlying supersymmetry -- a single Hermitian supercharge. We derive a BPS bound for the masses of these solutions and construct a solution explicitly in a special case. The relevance to the confining phase of N=1 SUSY Yang-Mills and the M-theory/SYM relationship is discussed.

Domain Wall Junctions are 1/4-BPS States

TL;DR

This work shows that theories with multiple vacua admit -BPS domain wall junctions preserving a single Hermitian supercharge, and derives both local and integral BPS bounds that constrain wall networks. It develops a long-distance, contour-based formulation of the BPS conditions and provides explicit constructions in the and models, including a closed-form for a four-wall junction and a real, positive-definite Kähler metric realization. The analysis connects to the confining phase of SYM and to M-theory dual descriptions, predicting junction states in SYM and offering concrete holographic avenues via brane intersections. Overall, the paper establishes a robust framework for analyzing and constructing 1/4-BPS wall junctions, linking field-theoretic solitons to geometric and duality-inspired pictures with potential experimental relevance in nonperturbative SUSY dynamics.

Abstract

We study N=1 SUSY theories in four dimensions with multiple discrete vacua, which admit solitonic solutions describing segments of domain walls meeting at one-dimensional junctions. We show that there exist solutions preserving one quarter of the underlying supersymmetry -- a single Hermitian supercharge. We derive a BPS bound for the masses of these solutions and construct a solution explicitly in a special case. The relevance to the confining phase of N=1 SUSY Yang-Mills and the M-theory/SYM relationship is discussed.

Paper Structure

This paper contains 8 sections, 35 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Supersymmetric Domain Walls
  3. BPS bounds for junctions
  4. Domain wall junctions: the $Z_3$ case
  5. Long distance limit and integral BPS equations
  6. Geometric reverse-engineering: an explicit construction
  7. Relevance to $N=1$ SYM
  8. Discussion

Figures (4)

  • Figure 1: A field configuration that interpolates among the three supersymmetric vacua. The energy density is concentrated inside the contour.
  • Figure 2: A long-distance view of a three-wall junction, and three elongated rectangular contours in the $z-\bar{z}$ plane.
  • Figure 3: In the $Z_4$ theory, the long-distance limit suggests the existence of a one-dimensional moduli space of BPS wall junction networks with four external walls. The two branches of moduli space, which meet at a $Z_4$-symmetric branch point, resemble t- and s-channel Feynman diagrams, respectively.
  • Figure 4: BPS polygons in the $W$-plane for the two examples discussed in this section. Vertices (vacua) preserve four supercharges, edges (half-walls) preserve two, and the interior (the junction) preserves one.