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arXiv · 1611.08926

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

Mario Garcia-Fernandez
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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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Mario Garcia-Fernandez. 2016-11-27. Ricci flow, Killing spinors, and T-duality in generalized geometry. https://arxiv.org/abs/1611.08926

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