Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions

Abstract

We study five dimensional AGT correspondence by means of the q-deformed beta-ensemble technique. We provide a special basis of states in the q-deformed CFT Hilbert space consisting of generalized Macdonald polynomials, derive the loop equations for the beta-ensemble and obtain the factorization formulas for the corresponding matrix elements. We prove the spectral duality for Nekrasov functions and discuss its meaning for conformal blocks. We also clarify the relation between topological strings and q-Liouville vertex operators.

22 pages, 1 figure, v2: typos corrected, a reference added

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• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• An elliptic Virasoro symmetry in 6d
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• Higgsed network calculus
• $q$-Virasoro modular double and 3d partition functions
• Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators
• Superintegrability as the hidden origin of Nekrasov calculus
• Solving q-Virasoro constraints
• Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• q-Vertex Operator from 5D Nekrasov Function
• Bootstrapping the $S^5$ partition function
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• The Condensate from Torus Knots
• Pentad and triangular structures behind the Racah matrices
• Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Quantum spectral curve for (q,t)-matrix model
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Matrix model and dimensions at hypercube vertices
• Proof of 5D $A_n$ AGT conjecture at $\beta =1$