{"title":"Quiver algebras and their representations for arbitrary quivers","authors":"Wei Li","doi":"10.1007/JHEP12(2024)089","DOIUrl":null,"url":null,"abstract":"<p>The quiver Yangians were originally defined for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds, and serve as BPS algebras of these systems. Their characters reproduce the unrefined BPS indices, which are related to classical Donaldson-Thomas (DT) invariants. We generalize this construction in two directions. First, we show that this definition extends to arbitrary quivers with potentials. Second, we explore how one can refine the characters of the quiver Yangian to incorporate the refined BPS indices, which are related to motivic DT invariants. We focus on two main classes of quivers: the BPS quivers of 4D <span>\\( \\mathcal{N} \\)</span> = 2 theories and the quivers from the knot-quiver correspondence. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2024 12","pages":""},"PeriodicalIF":5.4000,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP12(2024)089.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of High Energy Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/JHEP12(2024)089","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
The quiver Yangians were originally defined for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds, and serve as BPS algebras of these systems. Their characters reproduce the unrefined BPS indices, which are related to classical Donaldson-Thomas (DT) invariants. We generalize this construction in two directions. First, we show that this definition extends to arbitrary quivers with potentials. Second, we explore how one can refine the characters of the quiver Yangian to incorporate the refined BPS indices, which are related to motivic DT invariants. We focus on two main classes of quivers: the BPS quivers of 4D \( \mathcal{N} \) = 2 theories and the quivers from the knot-quiver correspondence. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies.
期刊介绍：
The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal.
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Mostly Strong Interactions
Quantum Field Theory (phenomenology)
Strings and Branes
Phenomenological Aspects of Supersymmetry
Mostly Strong Interactions (phenomenology).
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