The Hull-Strominger system and the Anomaly flow on a class of solvmanifolds

TL;DR

This paper investigates the Hull-Strominger system and the Anomaly flow on a specific class of solvmanifolds, providing characterizations of solutions, analyzing flow behavior, and establishing convergence to Kähler metrics under certain conditions.

Contribution

It characterizes invariant solutions to the Hull-Strominger system on almost-abelian Lie groups and analyzes the flow dynamics, including conditions for convergence to Kähler metrics.

Findings

Invariant solutions characterized for the Hull-Strominger system.

Anomaly flow reduces to a simplified form on these solvmanifolds.

Flow is shown to be immortal and converges to Kähler metrics under specific assumptions.

Abstract

We study the Hull-Strominger system and the Anomaly flow on a special class of 2-step solvmanifolds, namely the class of almost-abelian Lie groups. In this setting, we characterize the existence of invariant solutions to the Hull-Strominger system with respect to the family of Gauduchon connections in the anomaly cancellation equation. Then, motivated by the results on the Anomaly flow, we investigate the flow of invariant metrics in our setting, proving that it always reduces to a flow of a special form. Finally, under an extra assumption on the initial metrics, we show that the flow is immortal and, when the slope parameter is zero, it always converges to a K\"ahler metric