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

2016/11/27 by Mario Garcia-Fernandez, Mario García-Fernández, Garcia-Fernandez, Mario · 7 citations
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Black Holes and Theoretical Physics

paper · doi:10.1016/j.aim.2019.04.038

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.

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