Geometric Couplings and Brane Supersymmetry Breaking

TL;DR

This work extends the geometric understanding of brane supersymmetry breaking by showing that, in the 10D Sugimoto model, all low-energy couplings can be recast as geometric dressings of bulk fields when formulated in the dual 6-form description, mapping Chern–Simons terms to Wess–Zumino terms. It further analyzes six-dimensional brane-susy models, where both Chern–Simons and Wess–Zumino terms are present, revealing that full geometrization is not possible in general, though the field equations retain a geometric form under certain conditions and via PST treatment of self-dual tensors. Across dimensions, a consistent goldstino sector is identified, with the dilaton tadpole a common feature signaling non-maximal vacua. The results point toward potential applications in four-dimensional brane-worlds and underscore the role of non-linear SUSY in coupling bulk and brane sectors.

Abstract

Orientifold vacua allow the simultaneous presence of supersymmetric bulks, with one or more gravitinos, and non-supersymmetric combinations of BPS branes. This ``brane supersymmetry breaking'' raises the issue of consistency for the resulting gravitino couplings, and Dudas and Mourad recently provided convincing arguments to this effect for the ten-dimensional $USp(32)$ model. These rely on a non-linear realization of local supersymmetry {\it à la} Volkov-Akulov, although no gravitino mass term is present, and the couplings have a nice geometrical interpretation in terms of ``dressed'' bulk fields, aside from a Wess-Zumino-like term, resulting from the supersymmetrization of the Chern-Simons couplings. Here we show that {\it all} couplings can be given a geometrical interpretation, albeit in the dual 6-form model, whose bulk includes a Wess-Zumino term, so that the non-geometric ones are in fact demanded by the geometrization of their duals. We also determine the low-energy couplings for six-dimensional (1,0) models with brane supersymmetry breaking. Since these include both Chern-Simons and Wess-Zumino terms, only the resulting field equations are geometrical, aside from contributions due to vectors of supersymmetric sectors.