Coherent states in quantum W1+∞ algebra and qq-character for 5d super Yang-Mills

Abstract

The instanton partition functions of N = 1 5d super Yang–Mills are built using elements of the representation theory of quantum W1+∞ algebra: Gaiotto state, intertwiner, vertex operator. This algebra is also known under the names of Ding–Iohara–Miki and quantum toroidal gl (1) algebra. Exploiting the explicit action of the algebra on the partition function, we prove the regularity of the 5d qq-characters. These characters provide a solution to the Schwinger–Dyson equations, and they can also be interpreted as a quantum version of the Seiberg–Witten curve.