Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator
Abstract
The quantum toroidal algebra of gl1 provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed W-algebras including non-principal cases are obtained by gluing the quantum toroidal algebras of gl1. These algebras are expected to be related with 5d AGT correspondence. In this paper, we discuss quantum deformation of the W-algebras obtained from su(N) by the quantum Drinfeld-Sokolov reduction with su(2) embedding [N-1,1]. They were studied by Feigin and Semikhatov and we refer to them as Feigin-Semikhatov's W-algebras. We construct free field realization and find several quadratic relations. We also compare the norm of the Whittaker states with the instanton partition function under the presence of a simple surface operator in the N=3 case.