Gauge origami and quiver W-algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909208553717760 |
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| author | Kimura, Taro Noshita, Go |
| author_facet | Kimura, Taro Noshita, Go |
| contents | We explore the quantum algebraic formalism of the gauge origami system in $\mathbb{C}^{4}$, 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 $\mathfrak{gl}_{1}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08545 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gauge origami and quiver W-algebras Kimura, Taro Noshita, Go High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory We explore the quantum algebraic formalism of the gauge origami system in $\mathbb{C}^{4}$, 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 $\mathfrak{gl}_{1}$. 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. |
| title | Gauge origami and quiver W-algebras |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2310.08545 |