Eirik Svanes, University of Oxford
"SU(3)-Structures and the Heterotic String”
We will first consider the Strominger system derived from heterotic string compactifications on a six-dimensional space. By requiring supersymmetry, we show that the corresponding geometry is complex, where the complex structure is parallel with respect to the Bismut connection, which has totally antisymmetric torsion. Initially, the moduli space of such structures is infinite dimensional. However, a constraint from physics, a certain Bianchi Identity, serves to reduce the moduli space to a finite-dimensional one. Next, we consider generalisations of the Strominger system, and higher order corrections. We show that supersymmetry still requires a complex internal space, with the complex structures still parallel with respect to the Bismut connection. This relies heavily on an integrability result for compatibility between supersymmetry and the heterotic equations of motion, which we show holds true at this higher order as well.
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