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

TL;DR

This paper introduces a new symmetry in two-dimensional $(1,0)$ supersymmetric non-linear sigma-models that generalizes existing holonomy symmetries, accommodating fluxes and instantons, and explores its anomalies and consistency with heterotic supergravity.

Contribution

It presents a novel symmetry extending the special holonomy $W$-symmetry to include fluxes and instantons, with analysis of anomalies and supergravity compatibility.

Findings

The new symmetry generalizes the $W$-symmetry to models with flux and instantons.

Cohomologically non-trivial quantum terms are invariant under the corrected symmetry.

The symmetry is consistent with heterotic supergravity at first order in $eta'$.

Abstract

A new symmetry of $(1,0)$ supersymmetric non-linear $\sigma$-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 $\mathcal{M}$. Our symmetry allows in particular non-trivial flux and instanton-like connections on vector bundles over $\mathcal{M}$. 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 $\alpha'$ is manifest and discussed.