Elliptic quantum toroidal algebra Uq,t,p(gl1,tor) and affine quiver gauge theories

We introduce a new elliptic quantum toroidal algebra U q , t , p ( gl 1 , t o r ) . Various representations in the quantum toroidal algebra U q , t ( gl 1 , t o r ) are extended to the elliptic case including the level (0,0) representation realized by using the elliptic Ruijsenaars difference operat...

Full description

Saved in:
Bibliographic Details
Published in:Letters in mathematical physics 2023-03, Vol.113 (2)
Main Authors: Konno, Hitoshi, Oshima, Kazuyuki
Format: Article
Language:English
Subjects:
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce a new elliptic quantum toroidal algebra U q , t , p ( gl 1 , t o r ) . Various representations in the quantum toroidal algebra U q , t ( gl 1 , t o r ) are extended to the elliptic case including the level (0,0) representation realized by using the elliptic Ruijsenaars difference operator. Various intertwining operators of U q , t , p ( gl 1 , t o r ) -modules w.r.t. the Drinfeld comultiplication are also constructed. We show that U q , t , p ( gl 1 , t o r ) gives a realization of the affine quiver W -algebra W q , t ( Γ ( A ^ 0 ) ) proposed by Kimura–Pestun. This realization turns out to be useful to derive the Nekrasov instanton partition functions, i.e., the χ y - and elliptic genus, of the 5d and 6d lifts of the 4d N = 2 ∗ U ( M ) theories and provide a new Alday–Gaiotto–Tachikawa correspondence.
ISSN:1573-0530
DOI:10.1007/s11005-023-01650-6