Consistent gravitino couplings in non-supersymmetric strings

TL;DR

The paper addresses the apparent inconsistency of gravitino interactions in the 10d USp(32) Type I string, where a massless gravitino coexists with non-supersymmetric open-sector matter. It argues for a local supersymmetry that is non-linearly realized in the open sector and derives the leading low-energy Lagrangian describing N=1 supergravity coupled to non-supersymmetric Yang-Mills matter, with a goldstino-like singlet playing a central role. By incorporating dilaton tadpoles and a Green–Schwarz anomaly-cancellation mechanism, the authors construct a complete, supersymmetric EFT including Chern–Simons terms, ensuring consistent gravitino dynamics. The results suggest a broader applicability to lower-dimensional Type I models with non-supersymmetric branes and potential brane-world implications, supported by consistency checks against string amplitudes.

Abstract

The massless spectrum of the ten dimensional USp(32) type I string has an N=1 supergravity multiplet coupled to non-supersymmetric matter. This raises the question of the consistency of the gravitino interactions. We resolve this apparent puzzle by arguing for the existence of a local supersymmetry which is non-linearly realised in the open sector. We determine the leading order low energy effective Lagrangian. Similar results are expected to apply to lower dimensional type I models where supergravity is coupled to non-supersymmetric branes.