No-scale supersymmetry breaking vacua and soft terms with torsion

TL;DR

The paper advances the study of no-scale supersymmetry breaking vacua in Type II string theory by analyzing compactifications on SU(3)-structure manifolds with intrinsic torsion and orientifold planes. It identifies two distinct no-scale breaking mechanisms—quaternionic breaking, mediated by hypermultiplet moduli, and mixed breaking, linked to Scherk–Schwarz-like setups with vector multiplet involvement—and provides explicit constructions in IIB and IIA, including concretely computed geometrically induced μ-terms on twisted-tori. The authors also derive soft-terms on D-branes, revealing rich patterns controlled by the torsion and flux data, with detailed tables for D9/D5/D6 (and their duals) in the quaternionic and mixed cases. These results offer structured avenues for model-building in string phenomenology and highlight the role of geometric fluxes in shaping the visible-sector spectrum, while noting the need to incorporate non-perturbative effects to address flat directions and potential instabilities. The work thereby broadens the landscape of no-scale vacua beyond Calabi–Yau Calabi–Yau orientifolds to SU(3)-structure geometries with intrinsic torsion, elucidating the interplay between bulk moduli, brane dynamics, and low-energy soft terms.

Abstract

We analyze the conditions to have no-scale supersymmetry breaking solutions of type IIA and IIB supergravity compactified on manifolds of SU(3)-structure. The supersymmetry is spontaneously broken by the intrinsic torsion of the internal space. For type IIB orientifolds with O9 and O5-planes the mass of the gravitino is governed by the torsion class W_1, and the breaking is mediated through F-terms associated to descendants of the original N=2 hypermultiplets. For type IIA orientifolds with O6-planes we find two families of solutions, depending on whether the breaking is mediated exclusively by hypermultiplets or by a mixture of hypermultiplets and vector multiplets, the latter case corresponding to a class of Scherk-Schwarz compactifications not dual to any geometric IIB setup. We compute the geometrically induced mu-terms for D5, D6 and D9-branes on twisted tori, and discuss the patterns of soft-terms which arise for pure moduli mediation in each type of breaking. As for D3 and D7-branes in presence of 3-form fluxes, the effective scalar potential turns out to possess interesting phenomenological properties.