5D AGT conjecture for circular quivers

Abstract

The best way to represent generic conformal blocks is provided by the free-field formalism, where they acquire a form of multiple Dotsenko-Fateev-like integrals of the screening operators. Degenerate conformal blocks can be described by the same integrals with special choice of parameters. Integrals satisfy various recurrent relations, which for the special choice of parameters reduce to closed equations. This setting is widely used in explaining the AGT relation, because similar integral representations exist also for Nekrasov functions. We extend this approach to the case of q-Virasoro conformal blocks on elliptic surface -- generic and degenerate. For the generic case, we check equivalence with instanton partition function of a 5d circular quiver gauge theory. For the degenerate case, we check equivalence with partition function of a defect in the same theory, also known as the Shiraishi function. We find agreement in both cases. This opens a way to re-derive the sophisticated equation for the Shiraishi function as the equation for the corresponding integral, what seems straightforward, but remains technically involved and is left for the future.

13 pages, 3 figures

References in corpus (21)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• 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)
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• 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
• A direct proof of AGT conjecture at beta = 1
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Check of AGT Relation for Conformal Blocks on Sphere
• Generalized matrix models and AGT correspondence at all genera
• The Quantum DELL System
• Seiberg-Witten curve via generalized matrix model
• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Superintegrability as the hidden origin of Nekrasov calculus
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• On the status of DELL systems
• Non-stationary difference equation for q-Virasoro conformal blocks
• Diamond of triads