English

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

High Energy Physics - Theory 2024-10-25 v2 Mathematical Physics math.MP

Abstract

In this paper, we give a proof of 5D AnA_n AGT conjecture at β=1\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 AnA_n Selberg integral, which generalizes the AnA_n Selberg integral and the q-deformed A1A_1 Selberg integral in the literature. A q-deformed AnA_n Selberg average formula with n+1n+1 Schur polynomials is proposed and proved to complete the proof.

Keywords

Cite

@article{arxiv.2405.13676,
  title  = {Proof of 5D $A_n$ AGT conjecture at $\beta=1$},
  author = {Qian Shen and Zi-Hao Huang and Shao-Ping Hu and Qing-Jie Yuan and Kilar Zhang},
  journal= {arXiv preprint arXiv:2405.13676},
  year   = {2024}
}

Comments

19 pages; v2: published version, with the conjecture for the q-deformed $A_n$ Selberg average formula of $n+1$ Schur polynomials proved