Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra
AbstractWe derive the generalization of the Knizhnik-Zamolodchikov equation (KZE) associated with the Ding-Iohara-Miki algebra Uq,t(gl^^1). We demonstrate that certain refined topological string amplitudes satisfy these equations and find that the braiding transformations are performed by the R matrix of Uq,t(gl^^1). The resulting system is the uplifting of the u^1 Wess-Zumino-Witten model. The solutions to the (q,t) KZE are identified with the (spectral dual of) building blocks of the Nekrasov partition function for five-dimensional linear quiver gauge theories. We also construct an elliptic version of the KZE and discuss its modular and monodromy properties, the latter being related to a dual version of the KZE.