A goldstino at the bottom of the cascade

TL;DR

This work examines how spontaneous supersymmetry breaking can arise in the KS conifold cascade by employing a five‑dimensional N=2 truncation of type IIB supergravity on T^{1,1}. It derives holographic Ward identities for the KS system and shows that a goldstino mode appears only on the vacuum corresponding to antiD3‑brane at the conifold tip, as signaled by a nonzero vacuum energy and specific operator VEVs. The analysis demonstrates that these identities hold generically, independent of IR singularities, and clarifies the role of the operator O_{tilde b} in the SUSY‑breaking trace relation. Together with a detailed mapping of bulk fields to QFT operators and a careful holographic renormalization, the paper provides a robust framework for diagnosing spontaneous SUSY breaking in cascading gauge theories and offers a general methodology applicable to similar holographic models.

Abstract

Working within a five-dimensional consistent truncation of type IIB supergravity dimensionally reduced on $T^{1,1}$, we consider supersymmetry breaking solutions with the asymptotics of the supersymmetric Klebanov-Strassler background. There exists a two-parameter family of such solutions. Within this family, we show that those (and only those) solutions related to antiD-branes at the tip of the conifold correspond to dual field theory vacua where a goldstino mode is present and supercurrent Ward identities hold. Our findings do not depend on the IR singularity of the dual backgrounds, nor on its resolution. As such, they constitute an independent, necessary check for the existence of supersymmetry breaking vacua in the conifold cascading gauge theory. Our analysis relies on a holographic derivation of the Ward identities which has a wider applicability, beyond the specific system and symmetries considered here.