Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator
arXiv:2005.14174
Abstract
The quantum toroidal algebra of 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 . These algebras are expected to be related with 5d AGT correspondence. In this paper, we discuss quantum deformation of the W-algebras obtained from 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.
arXiv comment44pages, v2: added references
References in corpus (28)
- Liouville Correlation Functions from Four-dimensional Gauge Theories
- A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
- Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
- Loop and surface operators in N=2 gauge theory and Liouville modular geometry
- Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
- Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
- Quantum Groups and Quantum Cohomology
- Asymptotically free N=2 theories and irregular conformal blocks
- Para-Liouville/Toda central charges from M5-branes
- A & B model approaches to surface operators and Toda theories
- Deformations of W-algebras associated to simple Lie algebras
- algebras
- Cohomological Hall algebras, vertex algebras and instantons
- Webs of W-algebras
- -KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
- Plane partitions with a "pit": generating functions and representation theory
- Trialities of -algebras
- On W algebras commuting with a set of screenings
- Duality of subregular W-algebras and principal W-superalgebras
- Kernel function and quantum algebras
- Integrals of motion from quantum toroidal algebras
- Quantum toroidal gl(1) and Bethe ansatz
- Correspondences among CFTs with different W-algebra symmetry
- Plane Partition Realization of (Web of) W-algebra Minimal Models
- Quadratic relations of the deformed -superalgebra
- The Integrals of Motion for the Deformed Virasoro Algebra
- Free field realization of -deformed primary fields for $U_q(\widehat{\sl}_2)$
- Free Boson Representation of