Abstract
We propose a set of novel expansions of Nekrasov’s instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on \( {\mathrm{\mathbb{C}}}_{q,{t}^{-1}}^2\times {\mathbb{S}}^1 \), we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces \( {\mathrm{\mathbb{C}}}_q\times {\mathbb{S}}^1 \), \( {\mathrm{\mathbb{C}}}_{t^{-1}}\times {\mathbb{S}}^1 \) and their intersection along \( {\mathbb{S}}^1 \). These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with Wq,t correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.
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Nieri, F., Pan, Y. & Zabzine, M. 3d expansions of 5d instanton partition functions. J. High Energ. Phys. 2018, 92 (2018). https://doi.org/10.1007/JHEP04(2018)092
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DOI: https://doi.org/10.1007/JHEP04(2018)092