Explicit embeddings of the deformed Shatashvili-Vafa vertex algebra SV_a into superaffine vertex algebras and the chiral de Rham complex are constructed for G2-structures with torsion, with a proportional to the scalar torsion class.
Moduli of $G_2$ structures and the Strominger system in dimension 7
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abstract
We consider $G_2$ structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi identity. The resulting system of partial differential equations can be regarded as an analogue of the Strominger system in $7$-dimensions. We initiate the study of the moduli space of solutions and show that it is finite dimensional using elliptic operator theory. We also relate the associated geometric structures to generalized geometry.
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$\mathrm{G}_2$-structures with torsion and the deformed Shatashvili-Vafa vertex algebra
Explicit embeddings of the deformed Shatashvili-Vafa vertex algebra SV_a into superaffine vertex algebras and the chiral de Rham complex are constructed for G2-structures with torsion, with a proportional to the scalar torsion class.