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<p>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.</p>

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The 4-fold Pandharipande–Thomas vertex and Jeffrey–Kirwan residue

  • 期刊论文

  • 发表日期：

    2026年4月2日

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  • Taro Kimura,
  • Go Noshita

摘要

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.