Pluriclosed flow and the Hull-Strominger system
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 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 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.
Keywords
Cite
@article{arxiv.2408.11674,
title = {Pluriclosed flow and the Hull-Strominger system},
author = {Mario Garcia-Fernandez and Raul Gonzalez Molina and Jeffrey Streets},
journal= {arXiv preprint arXiv:2408.11674},
year = {2024}
}