Heterotic Flux Compactifications and Their Moduli

TL;DR

This paper investigates supersymmetric heterotic string compactifications with H-flux, analyzing conditions for metric moduli and their behavior under dualities, with implications for flux compactification stability.

Contribution

It provides necessary conditions for metric moduli in heterotic flux compactifications and explores their characterization via duality and twisted differential operators.

Findings

Identified conditions for metric moduli in H-flux backgrounds.

Demonstrated duality correspondence with IIB orientifold models.

Discussed moduli conditions using twisted differential operators.

Abstract

We study supersymmetric compactification to four dimensions with non-zero H-flux in heterotic string theory. The background metric is generically conformally balanced and can be conformally Kahler if the primitive part of the H-flux vanishes. Analyzing the linearized variational equations, we write down necessary conditions for the existence of moduli associated with the metric. In a heterotic model that is dual to a IIB compactification on an orientifold, we find the metric moduli in a fixed H-flux background via duality and check that they satisfy the required conditions. We also discuss expressing the conditions for moduli in a fixed flux background using twisted differential operators.