The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue
High Energy Physics - Theory
2026-04-03 v2 Mathematical Physics
Algebraic Geometry
Combinatorics
math.MP
Abstract
We present a contour integral formalism for computing the K-theoretic equivariant Pandharipande--Thomas (PT) 4-vertex. Within the Jeffrey--Kirwan (JK) residue framework, we show that the PT 4-vertex can be obtained from the same integrand as the Donaldson--Thomas (DT) 4-vertex by choosing a different reference vector. We illustrate the formalism through examples involving curves and surfaces on the 4-fold. Furthermore, we investigate the DT/PT correspondence for the 4-fold setting together with its higher rank and supergroup-like generalizations.
Keywords
Cite
@article{arxiv.2508.12128,
title = {The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue},
author = {Taro Kimura and Go Noshita},
journal= {arXiv preprint arXiv:2508.12128},
year = {2026}
}
Comments
55 pages, v2: accepted version