Cohomological Hall Algebras, Vertex Algebras and Instantons
| Autor: | Yaping Yang, Miroslav Rapčák, Yan Soibelman, Gufang Zhao |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Vertex (graph theory) Instanton Pure mathematics FOS: Physical sciences 01 natural sciences Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Vertex operator algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) Representation Theory (math.RT) 0101 mathematics Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematical Physics Mathematics Conjecture 010102 general mathematics Statistical and Nonlinear Physics Cohomology Moduli space High Energy Physics - Theory (hep-th) Hall algebra 010307 mathematical physics Yangian Mathematics - Representation Theory |
| Zdroj: | Communications in Mathematical Physics. 376:1803-1873 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-019-03575-5 |
| Popis: | We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of $\mathfrak{gl}(1)$. Based on that we derive the vertex algebra at the corner $\mathcal{W}_{r_1,r_2,r_3}$ of Gaiotto and Rapcak. We conjecture that our approach works for a big class of Calabi-Yau categories, including those associated with toric Calabi-Yau $3$-folds. Comment: 72 pages, 4 figures, v2: Added some clarifications and updated references 73 pages, 4 figures, v3: Corrected typos and clarified some minor points |
| Databáze: | OpenAIRE |
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