Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator

Harada, Koichi

doi:10.48550/arxiv.2005.14174

Cited by 3 publications

(3 citation statements)

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“…Each trivalent vertex corresponds to the corner VOA[27] and the glued algebra gives the web of W-algebras. See also[147] where examples for the gluing process were explicitly done in the trigonometric language.…”

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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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confidence: 99%

Gauge origami and quiver W-algebras

Kimura,

Noshita

2024

J. High Energ. Phys.

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“…For other developments of this direction, see also[10][11][12][13][14][15][16][17][18][19][20].2 See[37][38][39][40][41] for corner vertex operator algebras and their relation with affine Yangian gl 1 and W1+∞.For gluing of affine Yangian gl 1 , see also[42][43][44].…”

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A note on quiver quantum toroidal algebra

Noshita

Watanabe

2022

J. High Energ. Phys.

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Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian $$ \mathfrak{gl} $$ gl 1. The characteristic feature of the algebra is the action on BPS states for non-compact toric Calabi-Yau threefolds, which are in one-to-one correspondence with the crystal melting models. These algebras can be bootstrapped from the action on the crystals and have various truncations.In this paper, we propose a q-deformed version of the quiver Yangian, referred to as the quiver quantum toroidal algebra (QQTA). We examine some of the consistency conditions of the algebra. In particular, we show that QQTA is a Hopf superalgebra with a formal super coproduct, like known quantum toroidal algebras. QQTA contains an extra central charge C. When it is trivial (C = 1), QQTA has a representation acting on the three-dimensional crystals, like Li-Yamazaki’s quiver Yangian. While we focus on the toric Calabi-Yau threefolds without compact 4-cycles, our analysis can likely be generalized to all toric Calabi-Yau threefolds.

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A Note on Quiver Quantum Toroidal Algebra

Noshita,

Watanabe

2021

Preprint

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Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian. The characteristic feature of the algebra is the action on BPS states for non-compact toric Calabi-Yau threefolds, which are in one-to-one correspondence with the crystal melting models. These algebras can be bootstrapped from the action on the crystals and have various truncations.In this paper, we propose a q-deformed version of the quiver Yangian, referred to as the quiver quantum toroidal algebra (QQTA). We examine some of the consistency conditions of the algebra. In particular, we show that QQTA is a Hopf superalgebra with a formal super coproduct, like known quantum toroidal algebras. QQTA contains an extra central charge. When it is trivial, QQTA has the three-dimensional representation acting on the three-dimensional crystals, like Li-Yamazaki's quiver Yangian. When Calabi-Yau threefolds have compact 4-cycles, the action seems to have some inconsistency, whose nature is not clear at this moment.

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Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator

Cited by 3 publications

References 49 publications

Gauge origami and quiver W-algebras

Gauge origami and quiver W-algebras

A note on quiver quantum toroidal algebra

A Note on Quiver Quantum Toroidal Algebra

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