Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondence
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912400261775360 |
|---|---|
| author | Kimura, Taro Noshita, Go |
| author_facet | Kimura, Taro Noshita, Go |
| contents | We continue the study of generalized gauge theory called gauge origami, based on the quantum algebraic approach initiated in [arXiv:2310.08545]. In this article, we in particular explore the D2 brane system realized by the screened vertex operators of the corresponding W-algebra. The partition function of this system given by the corresponding conformal block is identified with the vertex function associated with quasimaps to Nakajima quiver varieties and generalizations, that plays a central role in the quantum $q$-Langlands correspondence. Based on the quantum algebraic perspective, we address three new aspects of the correspondence: (i) Direct equivalence between the electric and magnetic blocks by constructing stable envelopes from the chamber structure of the vertex operators, (ii) Double affine generalization of quantum $q$-Langlands correspondence, and (iii) Conformal block realization of the origami vertex function associated with intersection of quasimaps, that realizes the higher-rank multi-leg Pandharipande-Thomas vertices of 3-fold and 4-fold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondence Kimura, Taro Noshita, Go High Energy Physics - Theory Algebraic Geometry Quantum Algebra We continue the study of generalized gauge theory called gauge origami, based on the quantum algebraic approach initiated in [arXiv:2310.08545]. In this article, we in particular explore the D2 brane system realized by the screened vertex operators of the corresponding W-algebra. The partition function of this system given by the corresponding conformal block is identified with the vertex function associated with quasimaps to Nakajima quiver varieties and generalizations, that plays a central role in the quantum $q$-Langlands correspondence. Based on the quantum algebraic perspective, we address three new aspects of the correspondence: (i) Direct equivalence between the electric and magnetic blocks by constructing stable envelopes from the chamber structure of the vertex operators, (ii) Double affine generalization of quantum $q$-Langlands correspondence, and (iii) Conformal block realization of the origami vertex function associated with intersection of quasimaps, that realizes the higher-rank multi-leg Pandharipande-Thomas vertices of 3-fold and 4-fold. |
| title | Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondence |
| topic | High Energy Physics - Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2404.17061 |