A bstract A new symmetry of (1 , 0) supersymmetric non-linear σ -models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy W -symmetry of Howe and Papadopoulos associated with structure group reductions of the target space ? $$ mathrm{mathcal{M}} $$ . Our symmetry allows in particular non-trivial flux and instanton-like connections on vector bundles over ? $$ mathrm{mathcal{M}} $$ . We also investigate potential anomalies and show that cohomologically non-trivial terms in the quantum effective action are invariant under a corrected version of our symmetry. Consistency with heterotic supergravity at first order in α ′ is manifest and discussed.
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