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On the 5-point conformal block with a level 2 degenerate field insertion and its AGT dual

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Pubblicato in:Journal of High Energy Physics vol. 2025, no. 10 (Oct 2025), p. 6
Autore principale: Poghosyan, Hasmik
Altri autori: Poghossian, Rubik
Pubblicazione:
Springer Nature B.V.
Soggetti:
Hypergeometric functions
Series expansion
Instantons
Differential equations
Gauge theory
Braiding
Partitions (mathematics)
Insertion
Recursive methods
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Abstract: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, which confirm our results.
ISSN:1029-8479
DOI:10.1007/JHEP10(2025)006
Fonte:Advanced Technologies & Aerospace Database