2025/04/16 by Hasmik Poghosyan, Poghosyan, Hasmik, Rubik Poghossian +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2504.11921
openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we develop and explore recursive methods to investigate the 2d CFT 5-point conformal block with a level 2 degenerate insertion, as well as its AGT dual, by solving the BPZ differential equation. First, we represent the solution of the differential equation as a double series expansion. On the 2-node quiver gauge theory side, this corresponds to the instanton series. We then demonstrate that the expansion coefficients are uniquely determined by a recursion relation. Inspired by the approach initiated in a paper by D. Gaiotto and J. Teschner, we partially resum this series and show that the result can be elegantly expressed in terms of a single hypergeometric function and its derivative. This new representation makes it straightforward to relate different asymptotic regions. As a by-product, this provides us a simple derivation of fusion and braiding coefficients. We describe the subtle procedure of merging the degenerate field with the outgoing state, thereby obtaining a generic 4-point block, which on the gauge theory side corresponds to the partition function of SU(2) gauge theory with four massive hypermultiplets in the Ω-background. Finally, we performed several nontrivial checks that confirm our results.