Exact solutions of domain wall junctions in arbitrary dimensions

Abstract

Exact analytic solutions of static, stable, nonplanar Bogomol'nyi-Prasad-Sommerfield (BPS) domain wall junctions are obtained in extended Abelian-Higgs models in (D þ 1)-dimensional spacetime. For specific choice of mass parameters, the Lagrangian is invariant under the symmetric group S Dþ1 of degree D þ 1 spontaneously broken down to S D in vacua, admitting S Dþ1 =S D domain wall junctions. In D ¼ 2, there are three vacua and three domain walls meeting at a junction point, in which the conventional topological charges Y and Z exist for the BPS domain wall junctions and the BPS domain walls, respectively, as known before. In D ¼ 3, there are four vacua, six domain walls, four junction lines on which three domain walls meet, and one junction point on which all the six domain walls meet. We define a new topological charge X for the junction point in addition to the conventional topological charges Y and Z. In general dimensions, we find that the configuration expressed in the D-dimensional real space is dual to a regular D-simplex in the D-dimensional internal space and that a d-dimensional subsimplex of the regular D-simplex corresponds to a (D − d)-dimensional intersection. Topological charges are generalized to the level-d wall charge W d for the d-dimensional subsimplexes.

Massless fermions and superconductivity of string-wall composites

“…There are several advantages: 1) the BPS solutions, no matter how complex they are, are given by the single gauge invariant scalar function Ω satisfying the master equation (2.25), 2) all the moduli are simply controlled by the moduli matrix H 0 . These have been already established in the literatures [24,25,29,40,41,44,47,48,[51][52][53][54][55][56][57][58][59][60][61]. In addition to these virtues, 3) we found in this paper that for any BPS background configurations the fermion zero mode function is analytically given by Ω −h/2 , see eq.…”

“…Therefore, the string-wall composites in the two different theories are indistinguishable by physical observables such as energy density and topological charge densities. Indeed, the overall constant shift has been ignored in the previous works [24,25,47,48]. Nevertheless, we will see in the next sections that in the presence of fermions coupled with ⃗ φ, the overall mass shift cannot be ignored.…”