Anomaly Cancellation and Smooth Non-Kahler Solutions in Heterotic String Theory

TL;DR

This paper constructs smooth heterotic string backgrounds as T^2 bundles over Calabi-Yau two-folds, emphasizing the role of anomaly cancellation which restricts the base to be K3, and verifies these solutions via duality with M-theory.

Contribution

It identifies conditions for anomaly cancellation in heterotic flux compactifications with T^2 bundle structures, leading to new smooth non-Kahler solutions with specific base restrictions.

Findings

Anomaly cancellation requires the base to be K3, excluding T^4.

Constructed explicit smooth solutions with T^2 bundle over Calabi-Yau two-folds.

Validated solutions through duality with M-theory flux backgrounds.

Abstract

We show that six-dimensional backgrounds that are T^2 bundle over a Calabi-Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can only be satisfied if the base is K3 while a T^4 base is excluded. The conditions imposed by anomaly cancellation for the T^2 bundle structure, the dilaton field, and the holomorphic stable bundles are analyzed and the solutions determined. Applying duality, we check the consistency of the anomaly cancellation constraints with those for flux backgrounds of M-theory on eight-manifolds.