On the KKLT Goldstino

TL;DR

This paper constructs and analyzes non-supersymmetric solutions in a string theory setup, providing evidence that the KKLT construction, if metastable, corresponds to a genuine spontaneous supersymmetry breaking vacuum.

Contribution

It generalizes previous supergravity solutions to include conifold deformations and identifies the nature of SUSY-breaking modes, confirming their spontaneous origin via holographic methods.

Findings

Only two SUSY-breaking modes are present.

One mode corresponds to spontaneous SUSY breaking.

Supports KKLT metastability as genuine spontaneous SUSY breaking.

Abstract

We construct general asymptotically Klebanov-Strassler solutions of a five dimensional $SU(2) \times SU(2) \times \mathbb{Z}_2\times \mathbb{Z}_{2R}$ truncation of IIB supergravity on $ T^{1,1} $, that break supersymmetry. This generalizes results in the literature for the $SU(2) \times SU(2) \times \mathbb{Z}_2\times U(1)_R$ case, to a truncation that is general enough to capture the deformation of the conifold in the IR. We observe that there are only two SUSY-breaking modes even in this generalized set up, and by holographically computing Ward identities, we confirm that only one of them corresponds to spontaneous breaking: this is the mode triggered by smeared anti-D3 branes at the tip of the warped throat. Along the way, we address some aspects of the holographic computation of one-point functions of marginal and relevant operators in the cascading gauge theory. Our results strengthen the evidence that {\it if} the KKLT construction is meta-stable, it is indeed a spontaneously SUSY-broken (and therefore bona fide) vacuum of string theory.