String Theory Realizations of the Nilpotent Goldstino

TL;DR

This work constructs explicit string-theory realizations of the nilpotent goldstino by placing a single anti-D3-brane on top of an O3-plane within warped, fluxed IIB throats. In the KS-like background with (2,1) ISD flux, the open-string spectrum reduces to a solitary massless fermion—the goldstino—consistent with a nilpotent chiral multiplet and the Volkov-Akulov description of spontaneously broken SUSY. The authors also explore how such setups can be embedded in more general warped geometries, including throats with O3-planes at their infrared tips and alternative O7-plane configurations, and discuss how the nilpotent sector couples to moduli and visible matter, yielding uplift terms and soft SUSY-breaking patterns. These results bolster the KKLT and related de Sitter stabilization schemes by providing a concrete microscopic origin for the nilpotent goldstino and outlining avenues for global model-building and phenomenology. Overall, the paper links explicit string constructions to low-energy effective descriptions of SUSY breaking, with potential implications for cosmology and particle phenomenology.

Abstract

We describe in detail how the spectrum of a single anti-D3-brane in four-dimensional orientifolded IIB string models reproduces precisely the field content of a nilpotent chiral superfield with the only physical component corresponding to the fermionic goldstino. In particular we explicitly consider a single anti-D3-brane on top of an O3-plane in warped throats, induced by $(2,1)$ fluxes. More general systems including several anti-branes and other orientifold planes are also discussed. This provides further evidence to the claim that non-linearly realized supersymmetry due to the presence of antibranes in string theory can be described by supersymmetric theories including nilpotent superfields. Implications to the KKLT and related scenarios of de Sitter moduli stabilization, to cosmology and to the structure of soft SUSY-breaking terms are briefly discussed.

Figures (8)

• Figure 1: The one-loop open string annulus and Moebius strip diagrams turn into closed string channel diagrams describing tree level exchange of NSNS and RR states between two boundaries (branes or antibranes), or between one boundary and one crosscap (O3-plane).
• Figure 2: a) The web diagram for the resolved conifold; the finite segment corresponds to the 2-sphere. b) The splitting of the diagram into sub-webs in equilibrium describes the complex deformation; the dashed segment measuring the sub-web separation represents the 3-sphere. c) The 3-sphere in the complex deformation can support fluxes which lead to the KS warped throat.
• Figure 3: Dimer diagram for the theory of D-branes at a conifold. The dashed line is the unit cell in the periodic array.
• Figure 4: a) Web diagram for the geometry $xy=z^3w^2$ in the resolved phase; the exponents of $z,w$ in the defining equation are related to the numbers of parallel vertical external legs. b) Diagram for the deformed geometry, with two independent 3-spheres, shown as dashed lines.
• Figure 5: Dimer diagram describing the gauge theory on D3-branes at the geometry $xy=z^3w^2$.