Gravity duals for little string theories—which give rise to four-dimensional theories that undergo permanent confinement in the infrared—have not been studied in great detail. We address this question in the framework of heterotic $SO(32)$ and $E_8\times E_8$ string theory, constructing these backgrounds by wrapping heterotic 5-branes on calibrated two-cycles of non-Kähler resolved conifolds. Related to deformations of the underlying little string theories, we find numerous analytic solutions preserving $\mathcal{N}=1$ supersymmetry in four dimensions. These theories all have non-Abelian global symmetries that generally arise from both the heterotic vector bundle and from certain orbifold states. In the decoupling limit, we argue that the gravity duals are given by non-Kähler manifolds that have both blown-up two-cycles and three-cycles at the origin. We argue this following certain duality sequences that include M-theory torsional manifolds at an intermediate step, which help us to construct new type ${\mathrm{I}}^{\prime }$ gauge/gravity duality pairs. In the M-theory duality frame, we also elucidate new sequences of flips and flops.

• Received 15 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.066003