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Weyl mutations in Quiver Yangians.

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Title: Weyl mutations in Quiver Yangians.
Authors: Galakhov, Dmitry1,2,3,4 (AUTHOR) d.galakhov.pion@gmail.com, Gavshin, Alexei1,2,4 (AUTHOR) gavshin.an@phystech.edu, Morozov, Alexei1,2,3,4 (AUTHOR) morozov@itep.ru
Source: European Physical Journal C -- Particles & Fields. May2026, Vol. 86 Issue 5, p1-39. 39p.
Subjects: Dynkin diagrams, Quantum groups, Equations, Calabi-Yau manifolds, D-branes, Yang-Mills theory, Moduli theory
Abstract: The problem of solving non-linear equations would be considerably simplified by a possibility to convert known solutions into the new ones. This could seem an element of art, but in the context of ADHM-like equations describing quiver varieties there is a systematic approach. In this note we study moduli spaces and dualities of quiver gauge theories associated to effective dynamics of D-branes compactified on Calabi-Yau resolutions. We concentrate on a subfamily of quivers Q g covering Dynkin diagrams for simple Lie algebras g , where the respective BPS algebra is expected to be the Yangian algebra Y (g) . For Yangians labeled by quivers their representations are described by solutions of ADHM-like equations. As quivers substitute Dynkin diagrams a generalization of the Weyl group W g acts on the ADHM solutions. Here we work with the case g = sl n + 1 and treat this group as a group of electro-magnetic Seiberg-like dualities (we call them Weyl mutations) on the respective quiver gauge theories. We lift it to the case of higher representations associated to rectangular Young diagrams. An action of Weyl mutations on the BPS Yangian algebra is also discussed. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. May2026, Vol. 86 Issue 5, p1-39. 39p.
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  Data: <searchLink fieldCode="DE" term="%22Dynkin+diagrams%22">Dynkin diagrams</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+groups%22">Quantum groups</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink><br /><searchLink fieldCode="DE" term="%22Calabi-Yau+manifolds%22">Calabi-Yau manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22D-branes%22">D-branes</searchLink><br /><searchLink fieldCode="DE" term="%22Yang-Mills+theory%22">Yang-Mills theory</searchLink><br /><searchLink fieldCode="DE" term="%22Moduli+theory%22">Moduli theory</searchLink>
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  Data: The problem of solving non-linear equations would be considerably simplified by a possibility to convert known solutions into the new ones. This could seem an element of art, but in the context of ADHM-like equations describing quiver varieties there is a systematic approach. In this note we study moduli spaces and dualities of quiver gauge theories associated to effective dynamics of D-branes compactified on Calabi-Yau resolutions. We concentrate on a subfamily of quivers Q g covering Dynkin diagrams for simple Lie algebras g , where the respective BPS algebra is expected to be the Yangian algebra Y (g) . For Yangians labeled by quivers their representations are described by solutions of ADHM-like equations. As quivers substitute Dynkin diagrams a generalization of the Weyl group W g acts on the ADHM solutions. Here we work with the case g = sl n + 1 and treat this group as a group of electro-magnetic Seiberg-like dualities (we call them Weyl mutations) on the respective quiver gauge theories. We lift it to the case of higher representations associated to rectangular Young diagrams. An action of Weyl mutations on the BPS Yangian algebra is also discussed. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1140/epjc/s10052-026-15678-0
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      – Code: eng
        Text: English
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        PageCount: 39
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      – SubjectFull: Dynkin diagrams
        Type: general
      – SubjectFull: Quantum groups
        Type: general
      – SubjectFull: Equations
        Type: general
      – SubjectFull: Calabi-Yau manifolds
        Type: general
      – SubjectFull: D-branes
        Type: general
      – SubjectFull: Yang-Mills theory
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      – SubjectFull: Moduli theory
        Type: general
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      – TitleFull: Weyl mutations in Quiver Yangians.
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            NameFull: Galakhov, Dmitry
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            NameFull: Gavshin, Alexei
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            NameFull: Morozov, Alexei
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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