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

Keywords

• Anomalies in Field and String Theories
• Conformal and W Symmetry
• Sigma Models
• Superstrings and Heterotic Strings