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Pré-Publication, Document De Travail Année : 2024

Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondence

Résumé

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.

Dates et versions

hal-04562224 , version 1 (29-04-2024)

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Taro Kimura, Go Noshita. Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondence. 2024. ⟨hal-04562224⟩
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