(q, t)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
Journal of High Energy Physics, 2018•Springer
A bstract We describe the general strategy for lifting the Wess-Zumino-Witten model from the
level of one-loop Kac-Moody\({U} _q {\left (\widehat {\mathfrak {g}}\right)} _k\) to generic
quantum toroidal algebras. A nearly exhaustive presentation is given for both\({U} _ {q, t}\left
({\widehat {\widehat {\mathfrak {gl}}}} _1\right)\) and\({U} _ {q, t}\left ({\widehat {\widehat
{\mathfrak {gl}}}} _n\right)\) when the screenings do not exist and thus all the correlators are
purely algebraic, ie do not include additional hypergeometric type integrations/summations.
level of one-loop Kac-Moody\({U} _q {\left (\widehat {\mathfrak {g}}\right)} _k\) to generic
quantum toroidal algebras. A nearly exhaustive presentation is given for both\({U} _ {q, t}\left
({\widehat {\widehat {\mathfrak {gl}}}} _1\right)\) and\({U} _ {q, t}\left ({\widehat {\widehat
{\mathfrak {gl}}}} _n\right)\) when the screenings do not exist and thus all the correlators are
purely algebraic, ie do not include additional hypergeometric type integrations/summations.
Abstract
We describe the general strategy for lifting the Wess-Zumino-Witten model from the level of one-loop Kac-Moody to generic quantum toroidal algebras. A nearly exhaustive presentation is given for both and when the screenings do not exist and thus all the correlators are purely algebraic, ie do not include additional hypergeometric type integrations/summations.
Springer