Line Operators in 3d Holomorphic QFT: Meromorphic Tensor Categories and dg-Shifted Yangians
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| Format: | Preprint |
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2025
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| author | Dimofte, Tudor Niu, Wenjun Py, Victor |
| author_facet | Dimofte, Tudor Niu, Wenjun Py, Victor |
| contents | We study line operators and their OPE's in perturbative 3d holomorphic-topological QFT's, including holomorphic-topological twists (quarter-BPS sectors) of 3d $N=2$ theories. In particular, we develop the representation theory of the category $C$ of perturbative line operators and its chiral tensor product, by generalizing techniques introduced by Costello and collaborators. We argue that lines are equivalent to modules for an $A_\infty$ algebra $A^!$ that's Koszul-dual to bulk local operators. We further establish a non-renormalization theorem for the OPE's of lines in a large class of theories (dubbed quasi-linear), allowing an exact resummation of quantum corrections. Based on physics arguments, we propose axioms for the full algebraic structure on $A^!$, calling it a "dg-shifted Yangian," which controls the OPE of lines. A key part of the structure is a Maurer-Cartan element $r(z)\in A^!\otimes A^!(\!(z^{-1})\!)$ that satisfies an $A_\infty$ generalization of the Yang-Baxter equation. As examples, we consider 3d $N=2$ gauge theories with arbitrary Chern-Simons levels, linear matter, and superpotential, and explicitly compute 1) perturbative bulk local operators (as $A_\infty$-chiral algebras); and 2) the Koszul-duals $A^!$ (proving they are dg-shifted Yangians). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Line Operators in 3d Holomorphic QFT: Meromorphic Tensor Categories and dg-Shifted Yangians Dimofte, Tudor Niu, Wenjun Py, Victor High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory We study line operators and their OPE's in perturbative 3d holomorphic-topological QFT's, including holomorphic-topological twists (quarter-BPS sectors) of 3d $N=2$ theories. In particular, we develop the representation theory of the category $C$ of perturbative line operators and its chiral tensor product, by generalizing techniques introduced by Costello and collaborators. We argue that lines are equivalent to modules for an $A_\infty$ algebra $A^!$ that's Koszul-dual to bulk local operators. We further establish a non-renormalization theorem for the OPE's of lines in a large class of theories (dubbed quasi-linear), allowing an exact resummation of quantum corrections. Based on physics arguments, we propose axioms for the full algebraic structure on $A^!$, calling it a "dg-shifted Yangian," which controls the OPE of lines. A key part of the structure is a Maurer-Cartan element $r(z)\in A^!\otimes A^!(\!(z^{-1})\!)$ that satisfies an $A_\infty$ generalization of the Yang-Baxter equation. As examples, we consider 3d $N=2$ gauge theories with arbitrary Chern-Simons levels, linear matter, and superpotential, and explicitly compute 1) perturbative bulk local operators (as $A_\infty$-chiral algebras); and 2) the Koszul-duals $A^!$ (proving they are dg-shifted Yangians). |
| title | Line Operators in 3d Holomorphic QFT: Meromorphic Tensor Categories and dg-Shifted Yangians |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2508.11749 |