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We obtain a family of heterotic supergravity backgrounds describingnon-Kahler warped conifolds with three-form flux and an Abelian gauge bundle,preserving N=1 supersymmetry in four dimensions. At large distance from thesingularity the usual Ricci-flat conifold is recovered. By performing a Z_2orbifold of the T^{1,1} base, the conifold singularity can be blown-up to afour-cycle, leading to a completely smooth geometry. Remarkably, the throatregions of the solutions, which can be isolated from the asymptotic Ricci-flatgeometry using a double-scaling limit, possess a worldsheet CFT description interms of heterotic cosets whose target space is the warped resolvedorbifoldized conifold. Thus this construction provides exact solutions of themodified Bianchi identity. By solving algebraically these CFTs we compute theexact tree-level heterotic string spectrum and describe worldsheetnon-perturbative effects. The holographic dual of these solutions, inparticular their confining behavior, and the embedding of these fluxedsingularities into heterotic compactifications with torsion are also discussed.

Heterotic Resolved Conifolds with Torsion, from Supergravity to CFT