Ricci flow, Killing spinors, and T-duality in generalized geometry

TL;DR

This paper develops a Ricci flow framework in generalized geometry, linking it with Killing spinor equations and T-duality, and demonstrates how T-duality generates new solutions relevant to string theory and special holonomy metrics.

Contribution

It introduces a Ricci flow in generalized geometry, connects it with Killing spinors, and shows T-duality preserves solutions, providing new insights into string theory and geometric structures.

Findings

T-duality exchanges solutions of Ricci flow and Killing spinor equations.

Hull-Strominger system solutions are preserved under T-duality.

Mathematical explanation for the dilaton shift in string theory.

Abstract

We introduce a notion of Ricci flow in generalized geometry, extending a previous definition by Gualtieri on exact Courant algebroids. Special stationary points of the flow are given by solutions to first-order differential equations, the Killing spinor equations, which encompass special holonomy metrics with solutions of the Hull-Strominger system. Our main result investigates a method to produce new solutions of the Ricci flow and the Killing spinor equations. For this, we consider T-duality between possibly topologically distinct torus bundles endowed with Courant structures, and demonstrate that solutions of the equations are exchanged under this symmetry. As applications, we give a mathematical explanation of the dilaton shift in string theory and prove that the Hull-Strominger system is preserved by T-duality.