Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

Abstract

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy $\SU(3)$ and solutions of the Strominger system.

48 pages. Section 5 and Appendix A from previous version have been suppressed and will appear elsewhere. Title slightly changed, references added, presentation improved. To appear in Math. Annal

References in corpus (30)

• Supergravity as Generalised Geometry I: Type II Theories
• Reduction of Courant algebroids and generalized complex structures
• Generalized complex geometry
• The Space of Kähler metrics (II)
• Vanishing Theorems and String Backgrounds
• Twisted differential String and Fivebrane structures
• Generalised geometry for string corrections
• Torsion-free generalized connections and Heterotic Supergravity
• A no-go theorem for string warped compactifications
• Heterotic supersymmetry, anomaly cancellation and equations of motion
• Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
• Algebroids, Heterotic Moduli Spaces and the Strominger System
• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton
• Leibniz algebroids, twistings and exceptional generalized geometry
• Local Heterotic Torsional Models
• Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds
• Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients
• On Regular Courant Algebroids
• Special metric structures and closed forms
• Heterotic Flux Compactifications and Their Moduli
• Generalized Kahler geometry
• On marginal deformations of (0,2) non-linear sigma models
• Moduli Space of Torsional Manifolds
• On astheno-Kaehler metrics
• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton
• Bn-generalized geometry and G2(2)-structures
• Matched pairs of Courant algebroids
• Holomorphic Deformations of Balanced Calabi-Yau $\partial \bar{\partial }$-Manifolds
• Deformations of complex structures and the coupled Kähler-Yang-Mills equations
• Calabi-Yau manifolds with $B$-fields

Cited by in corpus (27)

• Canonical metrics on holomorphic Courant algebroids
• Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_{\infty }$ algebra
• The infinitesimal moduli space of heterotic $G_2$ systems
• Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy
• Lectures on the Strominger system
• Heterotic backgrounds via generalised geometry: moment maps and moduli
• Holomorphic string algebroids
• Gauge theory for string algebroids
• Heterotic Quantum Cohomology
• On the Effective Field Theory of Heterotic Vacua
• Superpotential of Three Dimensional $\mathcal{N}=1$ Heterotic Supergravity
• The heterotic ${\mathrm{G}}_2$ system on contact Calabi--Yau $7$-manifolds
• Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Eigenvalues and eigenforms on Calabi-Yau threefolds
• Heterotic Line Bundle Models on Generalized Complete Intersection Calabi Yau Manifolds
• Special Lagrangian cycles and Calabi-Yau transitions
• Small gauge transformations and universal geometry in heterotic theories
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• The Fu-Yau equation in higher dimensions
• Moduli of $G_2$ structures and the Strominger system in dimension 7
• Spinors of real type as polyforms and the generalized Killing equation
• Balanced and Aeppli Parameters for the Heterotic Moduli
• Dissections and automorphisms of regular Courant algebroids
• String principal bundles and Courant algebroids
• Flat Generalized Connections on Courant Algebroids
• $Spin(7)$ Compactifications and 1/4-BPS Vacua in Heterotic Supergravity