Abstract
Exact analytic solutions of static, stable, non-planar BPS domain wall junctions are obtained in extended Abelian-Higgs models in $(D+1)$-dimensional spacetime. For specific choice of mass parameters, the Lagrangian is invariant under the symmetric group ${\cal S}_{D+1}$ of degree $D+1$ spontaneously broken down to ${\cal S}_D$ in vacua, admitting ${\cal S}_{D+1}/{\cal S}_D$ domain wall junctions. In $D=2$, 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 $D=3$, 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.
Highlights
In D 1⁄4 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
Domain walls are the simplest topological solitons separating discrete vacua or ground states [1,2,3], often created in phase transitions associated with spontaneous breakings of discrete symmetries [4,5] in various systems from small to large such as magnets [6], graphenes [7], carbon nanotubes, chiral p-wave superconductors [8], Bose-Einstein condensations of ultracold atomic gases [9], helium superfluids [10,11,12], nuclear matter [13,14], as well as quark matter [15] relevant for interior of neutron stars, and our Universe [4,16]
We study nonplanar BPS domain wall junctions in which three or more domain walls having angles meet at a point
Summary
Domain walls (or kinks) are the simplest topological solitons separating discrete vacua or ground states [1,2,3], often created in phase transitions associated with spontaneous breakings of discrete symmetries [4,5] in various systems from small to large such as magnets [6], graphenes [7], carbon nanotubes, chiral p-wave superconductors [8], Bose-Einstein condensations of ultracold atomic gases [9], helium superfluids [10,11,12], nuclear matter [13,14], as well as quark matter [15] relevant for interior of neutron stars, and our Universe [4,16]. Planer network of the domain walls and junctions were studied as non-BPS states in Refs. We construct a novel exact solution of the three-dimensional domain wall junction connecting the four different vacua for D 1⁄4 3. We construct an exact solution of a BPS SDþ1=SD domain wall junction in D þ 1-dimensional spacetime. The SDþ1=SD domain wall junction expressed in the real space is dual to a regular D-simplex in the internal space whose D þ 1 vertices correspond to the vacua. The Appendix summarizes explicit expression of the symmetric group S4 and the coset S4=S3
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