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Quiver algebras and their representations for arbitrary quivers
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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 correspond 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 explain how to define the characters to incorporate the refined BPS indices, which correspond 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.
Forward citations
Cited by 2 Pith papers
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Wild wall-crossing and symmetric quivers in 4d and 3d $\mathcal{N}=2$ field theories
The paper derives a tree-of-unlinkings formula for wild Donaldson-Thomas invariants of m-Kronecker quivers from wall-crossing identities rewritten through symmetric quivers and diagonalization.
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Weyl Mutations in Quiver Yangians
Weyl group reflections act as Seiberg-like dualities on A_n quiver gauge theories, mapping stability chambers to each other while conjecturally leaving the quiver Yangian Y(sl_{n+1}) invariant.
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