Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA

Abstract

We construct Gaiotto states with fundamental multiplets in $SU(N)$ gauge theories, in terms of the orthonormal basis of spherical degenerate double affine Hecke algebra (SH in short), the representations of which are equivalent to those of $W_n$ algebra with additional $U(1)$ current. The generalized Whittaker conditions are demonstrated under the action of SH, and further rewritten in terms of $W_n$ algebra. Our approach not only consists with the existing literature but also holds for general $SU(N)$ case.

20 pages, 2 figures; v2: minor modifications, typos corrected

References in corpus (3)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Virasoro constraint for Nekrasov instanton partition function

Cited by in corpus (10)

• Quantum toroidal algebras and solvable structures in gauge/string theory
• Virasoro irregular conformal block and beta deformed random matrix model
• On the Jeffrey-Kirwan residue of BCD-instantons
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Recursive Method for Nekrasov partition function for classical Lie groups
• ABCD of qq-characters
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Charge functions for odd dimensional partitions