$$ \mathcal{G} $$-structure symmetries and anomalies in (1, 0) non-linear σ-models

Abstract

Abstract 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 $$ \mathrm{\mathcal{M}} $$ ℳ . Our symmetry allows in particular non-trivial flux and instanton-like connections on vector bundles over $$ \mathrm{\mathcal{M}} $$ 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.