Heterotic resolved conifolds with torsion, from supergravity to CFT

Abstract

We obtain a family of heterotic supergravity backgrounds describing warped non-Kähler conifolds with three-form flux and an Abelian gauge bundle, preserving N = 1 supersymmetry in four dimensions. At large distance from the singularity the usual Ricciflat conifold is recovered. By performing a Z 2 orbifold of the T 1,1 base, the conifold singularity can be blown-up to a four-cycle, leading to a completely smooth geometry. Remarkably, the throat regions of the solutions, which can be isolated from the asymptotic Ricci-flat geometry using a double-scaling limit, possess a worldsheet cft description in terms of heterotic cosets whose target space is the warped resolved orbifoldized conifold. Thus this construction provides exact solutions of the modified Bianchi identity. By solving algebraically these cfts we compute the exact tree-level heterotic string spectrum and describe worldsheet non-perturbative effects. The holographic dual of these solutions, in particular their confining behavior, and the embedding of these fluxed singularities into heterotic compactifications with torsion are also discussed.

The Abelian heterotic conifold

“…Relation to Previous Works: There are very few articles pertaining to local heterotic supergravity solutions for local throat geometries in the literature. Following [20] which we have already mentioned, a further supergravity analysis on the conifold appeared in [26]. The solutions in that work have a singular dilaton in the IR and in our notation have (r 2 H 2 ) = 0, in addition they are performing a sort of expansion in small a = r 2 H 2 .…”

“…Our current work is very much in the same vein as [16,17] except that we will be studying heterotic strings, and that the main class of our solutions will require a Z 2 orbifold of the conifold. It builds on earlier articles by one of the authors [19,20], where solutions of this type, first based on Eguchi-Hanson space (hence providing local models of Fu-Yau compactifications, see also [21]), second on the conifold. An important step towards obtaining these solutions was to define a large charge limit, in which the contribution of the tangent bundle curvature to the Bianchi identity can be consistently neglected.…”

“…In the blow-down limit of the conifold, the E 8 × E 8 solution near the dilaton singularity is expected be lifted in M-theory to a smooth AdS 5 eleven-dimensional solution, dual to an N = 1 superconformal theory in four dimensions. In the Spin(32)/Z 2 theory the physics is very different; the resolved Z 2 orbifold of the conifold is expected to be dual to an N = 1 confining theory with matter; its field theory limit is appropriately described in the type I dual frame, where the confining string was identified in [20] as the fundamental string; in a way these solutions are heterotic versions of the Chamseddine-Volkov-Maldacena-Nuñez solution [23,24,17]. The more general solutions presented in the present article share the same qualitative features and enlarge significantly the parameter space of such holographically dual pairs.…”

Supersymmetric String Vacua with Torsion and Geometric Flows

“…Strominger [36], Dasgupta, Rajesh, and Sethi [7], Becker, Becker, Fu, Tseng, and Yau [3], Carlevaro and Israel [5], Andreas and Garcia-Fernandez [2], and others).…”

Heterotic Hyper-Kähler flux backgrounds

“…3 we have chosen to work with Hermitian gauge fields, normalized as Tr T α T β = 2δ αβ . 4 The volume form of a three-sphere is…”