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arXiv · 2405.13676

Proof of 5D $A_n$ AGT conjecture at $\beta=1$

Qian Shen·Zi-Hao Huang·Shao-Ping Hu·Qing-Jie Yuan·Kilar Zhang
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Abstract

In this paper, we give a proof of 5D $A_n$ AGT conjecture at $\beta=1$, where the gauge theory side is one dimension higher than the original 4D case, and corresponds to the q-deformation of the 2D conformal field theory side. We define a q-deformed $A_n$ Selberg integral, which generalizes the $A_n$ Selberg integral and the q-deformed $A_1$ Selberg integral in the literature. A q-deformed $A_n$ Selberg average formula with $n+1$ Schur polynomials is proposed and proved to complete the proof.

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Qian Shen, Zi-Hao Huang, Shao-Ping Hu, Qing-Jie Yuan, Kilar Zhang. 2024-05-22. Proof of 5D $A_n$ AGT conjecture at $\beta=1$. https://doi.org/10.1007/jhep09(2024)085

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