Duality covariant curvatures for the heterotic string

TL;DR

This paper develops duality covariant curvature tensors within double field theory, enabling new insights into heterotic string backgrounds and their geometric structures.

Contribution

It introduces a systematic construction of duality covariant curvatures using an auxiliary space, extending previous methods to heterotic/type I strings.

Findings

Constructed duality covariant curvature and torsion tensors.

Developed a framework that interpolates between cigar and trumpet backgrounds.

Extended the geometric approach to heterotic string theories.

Abstract

Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable $\sigma$-models. They are constructed systematically with the help of a larger, auxiliary space in a procedure inspired by Cartan geometry originally proposed by Pol\'a\v{c}ek and Siegel for bosonic strings. It pivots around a maximally isotropic group that captures the generalized structure group of the physical space. We show how dropping the isotropy condition on this group allows us to describe heterotic/type I strings. As an immediate application, we construct a new family of heterotic backgrounds that interpolates between the two-dimensional cigar and trumpet backgrounds.