Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 6

Deformations of holomorphic pairs and $2d$-$4d$ wall-crossing

Pages: 1705 – 1769



Veronica Fantini (SISSA, Trieste, Italy)


We show how wall-crossing formulas in coupled $2d$-$4d$ systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a holomorphic vector bundle. The main part of the paper studies the relation between scattering diagrams and deformations of holomorphic pairs, building on recent work by Chan, Conan Leung and Ma.

Published 30 June 2023