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arXiv · 1606.08020

Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and qq-character for 5d Super Yang-Mills

Jean-Emile Bourgine·Masayuki Fukuda·Yutaka Matsuo·Hong Zhang·Rui-Dong Zhu
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Abstract

The instanton partition functions of $\mathcal{N}=1$ 5d super Yang-Mills are built using elements of the representation theory of quantum $\mathcal{W}_{1+\infty}$ algebra: Gaiotto state, intertwiner, vertex operator. This algebra is also known under the names of Ding-Iohara-Miki and quantum toroidal $\widehat{\mathfrak{gl}}(1)$ 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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Jean-Emile Bourgine, Masayuki Fukuda, Yutaka Matsuo, Hong Zhang, Rui-Dong Zhu. 2016-06-26. Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and qq-character for 5d Super Yang-Mills. https://doi.org/10.1093/ptep/ptw165

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