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arXiv · 2512.23012

Wall-crossing for invariants of equivariant 3CY categories

Nikolas Kuhn·Henry Liu·Felix Thimm
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Abstract

We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wall-crossing framework arXiv:2111.04694, using the authors' symmetrized pullback technique to preserve the symmetry of the (almost-perfect) obstruction theories throughout. As an application, we define and study wall-crossings of simple type between operational equivariant Donaldson--Thomas (DT), Pandharipande--Thomas (PT), and Bryan--Steinberg (BS) vertices. In particular, we give an explicit DT/PT descendent vertex correspondence in the Calabi--Yau limit. As another application, we construct and prove wall-crossing formulas for operational refined semistable Vafa--Witten invariants.

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Nikolas Kuhn, Henry Liu, Felix Thimm. 2025-12-28. Wall-crossing for invariants of equivariant 3CY categories. https://arxiv.org/abs/2512.23012

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