We explore the connection between super \( \mathcal{W} \) -algebras ( \( \mathcal{SW} \) -algebras) and G-structures with torsion. The former are realised as symmetry algebras of strings with \( \mathcal{N} \) = (1, 0) supersymmetry on the worldsheet, while the latter are associated with generic string backgrounds with non-trivial Neveu-Schwarz flux H. In particular, we focus on manifolds featuring Spin(7), G2, SU(2), and SU(3)-structures. We compare the full quantum algebras with their classical limits, obtained by studying the commutators of superconformal and \( \mathcal{W} \) -symmetry transformations — which preserve the action of the (1, 0) non-linear σ-model. We show that, at first order in the string length scale ℓs, the torsion deforms some of the OPE coefficients corresponding to special holonomy through a scalar torsion class.
