Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

Abstract

Abstract. We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU (3) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain.

Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

“…For threefolds, Strominger described some perturbative solutions in [Str86]. Many years later, Li and Yau [LY05] obtained the first smooth irreducible solutions to the system for U (4) or U (5) principal bundles on Kähler Calabi-Yau manifolds, which was further developed in [AGF12]. As for non-Kähler Calabi-Yau inner spaces, the first solution was constructed by Fu and Yau [FY08].…”

New Examples of Stable Bundles on Calabi–Yau Three-Folds

“…Condition (10) is the integrability condition for the existence of a solution of the heterotic anomaly equation. For the case [W ] = 0 it has been shown that X and E can be deformed to a solution of the anomaly equation even already on the level of differential forms [16], [17] (generalizing results of [18], [19]). Thus it is of interest to see if a given stable vector bundle satisfies (10) and so provides a solution to the basic consistency constraint imposed by heterotic string theory.…”

Monad constructions of omalous bundles

“…Second, it was shown by Andreas and Garcia-Fernandez in [1] that stable omalous bundles over Calabi-Yau 3-folds admit solutions of the Strominger system, which is a system of coupled partial differential equations defined over a compact complex manifold relevant in heterotic string theory, c.f. [1] and the references therein.…”

“…The simplest example of omalous bundles are T X⊕O ⊕k X and its deformations; a few other examples were considered in [1,6,10,14]. Our goal is to construct more examples of (stable) omalous bundles over various choices for X using…”

“…(ii) Furthermore the omalous bundle E is stable for (d, l, c) = (3, 2, 1), (4,1,5) and semi-stable for (d, l, c) = (5, 0, 10).…”