Supersymmetric solutions on $SU(4)$-structure deformed Stenzel space

The Stenzel space fourfold is a noncompact Calabi-Yau (CY) which is a higher-dimensional analogue of the deformed conifold. We consider $\mathcal{N}=(1,1)$, type-IIA, $\mathcal{N}=1$ M-theory and $\mathcal{N}=(2,0)$, type-IIB compactifications on this Stenzel space, thus examining the gravity side of potentially higher-dimensional analogues of Klebanov-Strassler-like compactifications. We construct families of $SU(4)$-structures and solve associated moduli spaces, of complex and symplectic structures amongst others. By making use of these, we can construct IIA compactifications on manifolds homeomorphic to the Stenzel space fourfold, but with complex non-CY $SU(4)$-structures. Such compactifications are sourced by a distribution of NS5-branes. The external metric is asymptotically conformal ${\mathrm{AdS}}_3$ and should thus be suitable for holography applications.

Figure 1

The norm $j^2\equiv \star (dH\wedge \star dH)$ as a function of $\tau$ with $\lambda =1$ for the first example.

Figure 2

The norm $j^2$ as a function of $\tau$ with $\lambda =1$ for the second example.