Soliton Solutions of M-theory on an Orbifold

TL;DR

This work constructs explicit soliton solutions in the low-energy limit of M-theory on $S^1/Z_2$, including nonperturbative $κ^{2/3}$ corrections. It demonstrates that the orthogonal membrane is a BPS state preserving $1/4$ of the 11D supersymmetry (and $1/2$ on the hyperplanes), while parallel configurations break all supersymmetry; the same analysis for the 5-brane yields a BPS state for the parallel orientation but not for the orthogonal one. The gauge 5-brane is realized through boundary gauge instantons, yielding a nontrivial $x^{11}$-dependent strong-coupling dressing that reduces to the weakly coupled 10D gauge 5-brane in the appropriate limit. This provides the first explicit strongly coupled Horava–Witten solitons and clarifies the 11D–10D connection and duality to the heterotic string.

Abstract

We explicitly construct soliton solutions in the low energy description of M-theory on S^1/Z_2. It is shown that the 11-dimensional membrane is a BPS solution of this theory if stretched between the Z_2 hyperplanes. A similar statement holds for the 11-dimensional 5--brane oriented parallel to the hyperplanes. The parallel membrane and the orthogonal 5-brane, though solutions, break all supersymmetries. Furthermore, we construct the analog of the gauge 5-brane with gauge instantons on the hyperplanes. This solution varies nontrivially along the orbifold direction due to the gauge anomalies located on the orbifold hyperplanes. Its zero mode part is identical to the weakly coupled 10-dimensional gauge 5-brane.