Geometric Couplings and Brane Supersymmetry Breaking

TL;DR

This paper explores the geometric interpretation of couplings in brane supersymmetry breaking models, extending previous work to dual 6-form models and analyzing low-energy couplings in six-dimensional theories.

Contribution

It demonstrates that all couplings in brane supersymmetry breaking can be geometrically interpreted in the dual 6-form framework, including non-geometric ones, and determines low-energy couplings in 6D models.

Findings

All couplings can be geometrized in the dual 6-form model.

Non-geometric couplings are required by dualization.

Low-energy couplings in 6D models include Chern-Simons and Wess-Zumino terms.

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 \`a 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.