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arXiv · 2408.11674

Pluriclosed flow and the Hull-Strominger system

Mario Garcia-Fernandez·Raul Gonzalez Molina·Jeffrey Streets
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Abstract

We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the Hull-Strominger system. The evolution equations are derived using the theory of string algebroids, a class of Courant algebroids which occur naturally in higher gauge theory. Using this, we interpret the flow as generalized Ricci flow and also as a higher/coupled version of Hermitian-Yang-Mills flow, proving furthermore that it is compatible with symmetry reduction. Regarding our main analytical results, we prove a priori $C^{\infty}$ estimates for uniformly parabolic solutions. This in particular settles the question of smooth regularity of uniformly elliptic solutions of the Hull-Strominger system, generalizing Yau's $C^3$ estimate for the complex Monge-Amp\`ere equation. We prove global existence and convergence results for the flow on special backgrounds, and discuss a conjectural relationship of the flow to the geometrization of Reid's fantasy.

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Mario Garcia-Fernandez, Raul Gonzalez Molina, Jeffrey Streets. 2024-08-21. Pluriclosed flow and the Hull-Strominger system. https://arxiv.org/abs/2408.11674

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