Non-stationary difference equation for q-Virasoro conformal blocks
arXiv:2111.07939 · doi:10.1007/s11005-024-01856-2
Abstract
Conformal blocks of q,t-deformed Virasoro and W-algebras are important special functions in representation theory with applications in geometry and physics. In the Nekrasov-Shatashvili limit t -> 1, whenever one of the representations is degenerate then conformal block satisfies a difference equation with respect to the coordinate associated with that degenerate representation. This is a stationary Schrodinger equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generic t <> 1 is a non-stationary Schrodinger equation where t parametrizes shift in time. In this paper we make the non-stationary equation explicit for the q,t-Virasoro block with one degenerate and four generic Verma modules, and prove it when three modules out of five are degenerate, using occasional relation to Macdonald polynomials.
arXiv comment21 pages
References in corpus (27)
- Liouville Correlation Functions from Four-dimensional Gauge Theories
- Quantum Dilogarithm
- Quantization of Integrable Systems and Four Dimensional Gauge Theories
- Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
- Quantum Affine Algebras and Deformations of the Virasoro and W-algebras
- A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
- Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model
- Defects and Quantum Seiberg-Witten Geometry
- Affine SL(2) conformal blocks from 4d gauge theories
- Conformal blocks as Dotsenko-Fateev Integral Discriminants
- Proving AGT conjecture as HS duality: extension to five dimensions
- On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
- Five-dimensional AGT Relation and the Deformed beta-ensemble
- Instanton sums and five-dimensional gauge theories
- The Power of Nekrasov Functions
- Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model
- Towards Deformed Chiral Algebras
- On "Dotsenko-Fateev" representation of the toric conformal blocks
- Analyticity of Nekrasov Partition Functions
- Non-Abelian W-representation for GKM
- The Quantum DELL System
- On -representations of - and -deformed matrix models
- q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)
- Solving q-Virasoro constraints
- Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
- Basic Properties of Non-Stationary Ruijsenaars Functions
- Quantum spectral curve for (q,t)-matrix model