For G2 and SU(3) string backgrounds with NS flux, the scalar torsion class controls the first-order deformation of the worldsheet super W-algebra couplings away from special holonomy.
N=2 supersymmetric W-algebras
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We investigate extensions of the N=2 super Virasoro algebra by one additional super primary field and its charge conjugate. Using a supersymmetric covariant formalism we construct all N=2 super W-algebras up to spin 5/2 of the additional generator. Led by these first examples we close with some conjectures on the classification of N=2 ${\cal SW}(1,\Dt)$ algebras.
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$\mathcal{SW}$-algebras and strings with torsion
For G2 and SU(3) string backgrounds with NS flux, the scalar torsion class controls the first-order deformation of the worldsheet super W-algebra couplings away from special holonomy.