We construct the first known example of a near horizon supergravity solution for a pair of NS5-branes, intersecting on R-1.3 and localised in all directions except a single transverse circle. We do this by establishing an explicit map between the conifold metric and the near horizon geometry of two intersecting NS5-branes. clarifying and correcting a number of open issues in the literature en route. Our technique is general in nature and may be applied to a whole class of 1/4-BPS five-brane webs and their geometric duals. These 1/4-BPS solutions may have an interesting holographic interpretation in terms of little string theory.

We study a system of D-branes localized near an intersection of Neveu-Schwarz fivebranes, that is known to exhibit a landscape of supersymmetric and (metastable) supersymmetry breaking vacua. We show that early universe cosmology drives it to a particular long-lived supersymmetry breaking ground state.

Metastable supersymmetry breaking configurations of D-branes and NS5-branes in string theory often owe their existence to classical gravitational interactions between the branes. We show that in the effective theory of the light fields, these interactions give rise to a non-canonical Kähler potential and other D-terms. String theory provides a UV completion in which these non-renormalizable terms can be computed. We use these observations to clarify the relation between the phase structure of ISS-type models and their brane realizations.

In a previous paper, we used T-duality to construct a new type of 1/4-BPS solution describing a pair of NS5-branes intersecting in 1 + 3 dimensions and localized in all other directions except for a single transverse circle. This led to an explicit solution to a sourced Monge-Ampere equation, of which there are few known examples. In this paper, we refine this formalism and apply it to two important generalizations: the resolved and deformed conifolds. In doing so, we construct two new solutions describing, respectively, a pair of NS5-branes separated in a transverse direction and a pair of NS5-branes with a smooth 'diamond' profile. We show how the parameter of the resolved conifold (size of S²) maps to a transverse separation of the NS5-branes, while the modulus of the deformed conifold (size of S³) maps to the deformation parameter of the diamond web.