English

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