Non-supersymmetric infrared perturbations to the warped deformed conifold

Abstract

We analyze properties of non-supersymmetric, isometry-preserving perturbations to the infrared region of the warped deformed conifold, i.e. the Klebanov–Strassler solution. We discuss both perturbations that “squash” the geometry, so that the internal space is no longer conformally Calabi–Yau, and perturbations that do not squash the geometry. Among the perturbations that we discuss is the solution that describes the linearized near-tip backreaction of a smeared collection of D 3 ¯ -branes positioned in the deep infrared. Such a configuration is a candidate gravity dual of a non-supersymmetric state in a large-rank cascading gauge theory. Although D 3 ¯ -branes do not directly couple to the 3-form flux, we argue that, due to the presence of the background imaginary self-dual flux, D 3 ¯ -branes in the Klebanov–Strassler geometry necessarily produce singular non-imaginary self-dual flux. Moreover, since conformally Calabi–Yau geometries cannot be supported by non-imaginary self-dual flux, the D 3 ¯ -branes squash the geometry as our explicit solution shows. We also briefly discuss supersymmetry-breaking perturbations at large radii and the effect of the non-supersymmetric perturbations on the gravitino mass.