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

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

\mathrm {SU}(3)

and solutions of the Strominger system.

Note:

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

58D27
53D18
spinor: Killing
space: vector
integrability
geometry
moduli
any-dimensional
holonomy: SU(3)
string model: heterotic

References(72)

Figures(0)

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