Crystal melting, BPS quivers and plethystics

Bao, Jiakang; He, Yang‐Hui

doi:10.1007/jhep06(2022)016

Cited by 6 publications

(5 citation statements)

References 101 publications

(171 reference statements)

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“…They might also give possible truncations on the crystal. Moreover, it would be interesting to see whether other crystal configurations, such as crystals in other chambers [68][69][70] and 2d crystals [8,9,71], could give similar relations.…”

Section: Discussionmentioning

confidence: 99%

Quiver Yangians and -algebras for generalized conifolds

Bao

2023

J. Phys. A: Math. Theor.

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We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach by Guay-Nakajima-Wendlandt. We also prove that the quiver Yangians related by Seiberg duality are indeed isomorphic. Then we discuss their connections to $\mathcal{W}$-algebras analogous to the study by Ueda. In particular, the universal enveloping algebras of the $\mathcal{W}$-algebras are truncations of the quiver Yangians, and therefore they naturally have truncated crystals as their representations.

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Section: Discussionmentioning

confidence: 99%

Quiver Yangians and -algebras for generalized conifolds

Bao

2023

J. Phys. A: Math. Theor.

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“…Analogous to the Yangian algebras discussed above, for toric CYs without compact divisors whose quivers have more than two nodes, 17 the quiver Yangians are actually generated by finitely many generators.…”

Section: Generators Of Quiver Yangiansmentioning

confidence: 99%

“…The supersymmetric extension, namely the W N =2 1+∞ algebra, was then studied in [20,[30][31][32][33]. This supersymmetric version of the W algebra contains two commuting W 1+∞ algebras and can be constructed from gluing the two subalgebras with extra fermionic or bosonic generators (see also [17]). Hence, its representation theory can be nicely encoded by the twin plane partitions.…”

Section: Jhep08(2022)219mentioning

confidence: 99%

“…The realization of quiver Yangians should also incorporate the wall crossing phenomena [13,14]. The crystal configurations for different chambers have also been studied such as in [15][16][17]. In particular, the quiver Yangians were extended to the shifted quiver Yangians in [18] which provides a nice framework for the study of wall crossing and closed/open BPS states counting problems.…”

Section: Introductionmentioning

confidence: 99%

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A note on quiver Yangians and ℛ-matrices

Bao

2022

J. High Energ. Phys.

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“…Applications of these algebras to supersymmetric gauge theories were done in [166]. For general abelian orbifold cases such as X = C 3 /Z n or X = C 3 /(Z m × Z n ), the representations and some applications were studied in [72,75,129,167].…”

Section: Jhep05(2024)208mentioning

confidence: 99%

Gauge origami and quiver W-algebras

Kimura,

Noshita

2024

J. High Energ. Phys.

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We explore the quantum algebraic formalism of the gauge origami system in ℂ4, where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas have free field interpretations, leading to the operator formalism of qq-characters associated with each D-brane. The qq-characters of D2 and D4-branes correspond to screening charges and generators of the affine quiver W-algebra, respectively. On the other hand, the qq-characters of D6 and D8-branes represent novel types of qq-characters, where monomial terms are characterized by plane partitions and solid partitions. The composition of these qq-characters yields the instanton partition functions of the gauge origami system, eventually establishing the BPS/CFT correspondence.Additionally, we demonstrate that the fusion of qq-characters of D-branes in lower dimensions results in higher-dimensional D-brane qq-characters. We also investigate quadratic relations among these qq-characters. Furthermore, we explore the relationship with the representations, q-characters, and the Bethe ansatz equations of the quantum toroidal $$ {\mathfrak{gl}}_1 $$ gl 1 . This connection provides insights into the Bethe/Gauge correspondence of the gauge origami system from both gauge-theoretic and quantum-algebraic perspectives.We finally present conjectures regarding generalizations to general toric Calabi-Yau four-folds. These generalizations imply the existence of an extensive class of qq-characters, which we call BPS qq-characters. These BPS qq-characters offer a new systematic approach to derive a broader range of BPS/CFT correspondence and Bethe/Gauge correspondence.

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Crystal melting, BPS quivers and plethystics

Cited by 6 publications

References 101 publications

Quiver Yangians and -algebras for generalized conifolds

Quiver Yangians and -algebras for generalized conifolds

A note on quiver Yangians and ℛ-matrices

Gauge origami and quiver W-algebras

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