Solutions for Intersecting Domain Walls with Internal Structure in Six Dimensions from a Z_2 x Z_2-invariant Action

TL;DR

This paper constructs a six-dimensional scalar field model with intersecting domain walls, demonstrating analytic solutions, fermion localization at junctions, and scalar field trapping, advancing understanding of higher-dimensional defect structures.

Contribution

It introduces a Z_2 x Z_2-invariant scalar field theory with analytic solutions for intersecting domain walls and explores fermion and scalar localization mechanisms.

Findings

Analytic solutions for intersecting domain walls in six dimensions.

Fermion zero modes localized at domain-wall junctions.

Scalar fields can be localized on the walls.

Abstract

We present a generic Z_2 x Z_2-invariant scalar field theory with four real scalar fields in six-dimensional Minkowskian spacetime which yields solutions consisting of two intersecting domain-wall kinks which are each paired by fields with lump-like profiles. For a special parameter choice, analytic solutions can be obtained. We show that the Z_2 x Z_2 symmetry can be maintained while coupling fermions by introducing scalar Yukawa couplings to one kink-lump pair and six-dimensional pseudoscalar Yukawa couplings to the other, and we show that there exists a zero mode localized to the domain-wall junction in this case. We also show that scalar fields can be localized.