Analyticity and resurgence in wall-crossing formulas
Algebraic Geometry
2022-04-05 v3 High Energy Physics - Theory
Mathematical Physics
Complex Variables
math.MP
Symplectic Geometry
Abstract
We introduce the notion of analytic stability data on the Lie algebra of vector fields on a torus. We prove that the subspace of analytic stability data is open and closed in the topological space of all stability data. We formulate a general conjecture which explains how analytic stability data give rise to resurgent series. This conjecture is checked in several examples.
Keywords
Cite
@article{arxiv.2005.10651,
title = {Analyticity and resurgence in wall-crossing formulas},
author = {Maxim Kontsevich and Yan Soibelman},
journal= {arXiv preprint arXiv:2005.10651},
year = {2022}
}
Comments
Version 2 of the paper contains new Subsection 2.6 where the Support Property in families is discussed. New Section 5 is devoted to the interpretation of the analytic stability data in terms of analytic fiber bundles endowed with non-linear flat connections. Few typos have been corrected. Published in Letters in Math.Phys