Torsional Heterotic Geometries

TL;DR

This work develops a perturbative framework to construct torsional heterotic backgrounds by exploiting duality with type IIB orientifold flux compactifications and M-theory/F-theory data, with a special emphasis on using the ${\Omega_+}$ connection to satisfy the heterotic Bianchi identity. It shows how type IIB fluxes map to heterotic torsion through a sequence of dualities, leading to a class of semi-flat, elliptic-fibration based geometries that preserve $N=1$ supersymmetry in four dimensions under precise holomorphic moduli and ISD/primitive flux conditions. The authors also address the tadpole constraints and the gravitational contributions to the Bianchi identity, arguing that a perturbative solution exists whenever tadpoles cancel, and they explore extensions to non-geometric backgrounds with two holomorphic parameters. In the quantum regime, they discuss how NS5-branes on an elliptic space admit a quantum-exact metric capturing all corrections that break torus isometries, and outline a program to construct fully consistent complex-dimensional threefold backgrounds by gluing in known curved metrics to repair singularities. Overall, the paper expands the landscape of heterotic torsional geometries and connects them to duality-driven perturbative solutions and quantum-corrected metrics with potential phenomenological relevance.

Abstract

We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.