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.
Superconformal algebras for the Schoen Calabi-Yau manifold
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abstract
We revisit the proposal of arXiv:2104.05716 for the worldsheet description of string theory compactifications on special holonomy manifolds obtained via connected sums: the geometric construction corresponds to a diamond of inclusions of worldsheet algebras. We present new evidence for the proposal by considering compactifications on the Schoen Calabi-Yau manifold.
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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.