D-terms on the resolved conifold

TL;DR

The paper constructs a non-Calabi–Yau, warped resolved conifold background in type IIB with ISD $(1,2)$ flux and D7-branes that break supersymmetry spontaneously without generating a bulk cosmological constant. It shows that non-primitive flux on D7-branes yields a nonzero D-term, explicitly quantified, while the bulk potential remains zero due to the ISD condition. The authors embed the setup into F-theory, solving for a fourfold and identifying normalisable harmonic forms associated with the seven-branes, which lift the IIB fluxes to a non-primitive $(2,2)$ G-flux. They discuss cosmological applications, including non-Kähler compactifications and an inflationary scenario where D-term uplift competes with dilaton-driven forces, and outline supersymmetry-restoration mechanisms at the end of inflation to terminate the dynamics. Overall, the work connects non-supersymmetric flux compactifications to inflaton potential construction via D-terms, supported by an F-theory uplift and a roadmap toward compactification and inflationary model-building.

Abstract

We derive a novel deformation of the warped resolved conifold background with supersymmetry breaking ISD (1,2) fluxes by adding D7-branes to this type IIB theory. We find spontaneous supersymmetry breaking without generating a bulk cosmological constant. In the compactified form, our background will no longer be a Calabi-Yau manifold as it allows a non-vanishing first Chern class. In the presence of D7-branes the (1,2) fluxes can give rise to non-trivial D-terms. We study the Ouyang embedding of D7-branes in detail and find that in this case the D-terms are indeed non-zero. In the limit when we approach the singular conifold, the D-terms vanish for Ouyang's embedding, although supersymmetry appears to be broken. We also construct the F-theory lift of our background and demonstrate how these IIB (1,2) fluxes lift to non-primitive (2,2) flux on the fourfold. The seven branes correspond to normalisable harmonic forms. We briefly sketch a possible way to attain an inflaton potential in this background once extra D3-branes are introduced and point out some possibilities of restoring supersymmetry in our background that could in principle be used as the end point of the inflationary set-up. In a companion paper we will analyse in details the inflationary dynamics in this background.