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arxiv: 1606.08020 · v3 · pith:LHJVARVGnew · submitted 2016-06-26 · ✦ hep-th · math-ph· math.AG· math.MP· math.QA· math.RT

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 This is my paper
classification ✦ hep-th math-phmath.AGmath.MPmath.QAmath.RT
keywords algebraquantummathcalinftypartitionsuperyang-millsaction
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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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