5D AGT Conjecture for Circular Quivers Explored

This paper investigates the AGT correspondence, a relationship between conformal field theory and gauge theory, specifically in the context of 5-dimensional circular quiver gauge theories. It extends existing approaches using free-field formalism and integral representations to analyze both generic and degenerate conformal blocks on elliptic surfaces. The key contribution is the verification of equivalence between these conformal blocks and instanton partition functions and defect partition functions (Shiraishi functions) in the 5D gauge theory. This work provides a new perspective on deriving equations for Shiraishi functions.