Quiver algebras and their representations for arbitrary quivers

A bstract 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) in...

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Published inThe journal of high energy physics Vol. 2024; no. 12; pp. 89 - 118
Main Author Li, Wei
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 11.12.2024
Springer Nature B.V
SpringerOpen
Subjects
Algebra
Classical and Quantum Gravitation
Conformal and W Symmetry
Construction
Crystals
D-Branes
Elementary Particles
Invariants
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Supersymmetric Gauge Theory
D-Branes
Supersymmetric Gauge Theory
Conformal and W Symmetry
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Abstract A bstract 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 N = 2 theories and the quivers from the knot-quiver correspondence. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies.
AbstractList 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 N $$ \mathcal{N} $$ = 2 theories and the quivers from the knot-quiver correspondence. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies.
A bstract 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 N = 2 theories and the quivers from the knot-quiver correspondence. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies.
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 $$ \mathcal{N} $$ N = 2 theories and the quivers from the knot-quiver correspondence. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies.
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 N = 2 theories and the quivers from the knot-quiver correspondence. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies.
ArticleNumber 89
Author Li, Wei
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Snippet A bstract The quiver Yangians were originally defined for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds, and serve as...
The quiver Yangians were originally defined for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds, and serve as BPS...
Abstract The quiver Yangians were originally defined for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds, and serve as...
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SubjectTerms Algebra
Classical and Quantum Gravitation
Conformal and W Symmetry
Construction
Crystals
D-Branes
Elementary Particles
Invariants
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Supersymmetric Gauge Theory
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Title Quiver algebras and their representations for arbitrary quivers
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