Solutions for intersecting domain walls with internal structure in six dimensions from aZ2×Z2-invariant action

Abstract

We present a generic ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$-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 lumplike profiles. For a special parameter choice, analytic solutions can be obtained. We show that the ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ 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.