Coherent states in quantum W_1+∞ algebra and qq-character for 5d Super Yang-Mills

2016/06/30 by Jean-Emile Bourgine, Masayuki Fukuda, Yutaka Matsuo +2 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.AG #math.MP #math.QA #math.RT

paper · pdf · doi:10.1093/ptep/ptw165

published as Prog Theor Exp Phys (2016) · 45 pages, 2 figures (v2: references added)

arxiv created 2016/10/17 · arxiv updated 2019/12/06

Abstract

The instanton partition functions of N=1 5d super Yang-Mills are built using elements of the representation theory of quantum W_1+∞ algebra: Gaiotto state, intertwiner, vertex operator. This algebra is also known under the names of Ding-Iohara-Miki and quantum toroidal \widehat\mathfrakgl(1) algebra. Exploiting the explicit action of the algebra on the partition function, we prove the regularity of the 5d qq-characters. These characters provide a solution to the Schwinger-Dyson equations, and they can also be interpreted as a quantum version of the Seiberg-Witten curve.

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