Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911365111742464 |
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| author | Kimura, Taro Noshita, Go |
| author_facet | Kimura, Taro Noshita, Go |
| contents | We develop a contour integral formalism for computing the K-theoretic equivariant 3-vertex. Within the Jeffrey--Kirwan (JK) residue framework, we show that, by an appropriate choice of the reference vector, both the equivariant Donaldson--Thomas (DT) and Pandharipande--Thomas (PT) 3-vertices can be extracted from the same integrand. We analyze three distinct limits of the PT 3-vertex, recovering the unrefined topological vertex, the refined topological vertex, and the Macdonald refined topological vertex. Higher-rank extensions of PT counting and the DT/PT correspondence are also explored. From a quantum algebraic perspective, we construct an operator version of the equivariant PT 3-vertex and term it the Pandharipande--Thomas $qq$-character. We then discuss its connection with the quantum toroidal $\mathfrak{gl}_{1}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters Kimura, Taro Noshita, Go High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory We develop a contour integral formalism for computing the K-theoretic equivariant 3-vertex. Within the Jeffrey--Kirwan (JK) residue framework, we show that, by an appropriate choice of the reference vector, both the equivariant Donaldson--Thomas (DT) and Pandharipande--Thomas (PT) 3-vertices can be extracted from the same integrand. We analyze three distinct limits of the PT 3-vertex, recovering the unrefined topological vertex, the refined topological vertex, and the Macdonald refined topological vertex. Higher-rank extensions of PT counting and the DT/PT correspondence are also explored. From a quantum algebraic perspective, we construct an operator version of the equivariant PT 3-vertex and term it the Pandharipande--Thomas $qq$-character. We then discuss its connection with the quantum toroidal $\mathfrak{gl}_{1}$. |
| title | Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2508.12125 |