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 ℂq,t−12×S1, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces ℂ q× S1, ℂt−1×S1 and their intersection along S1. 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.
3d expansions of 5d instanton partition functions
Nieri F.;
2018-01-01
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 ℂq,t−12×S1, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces ℂ q× S1, ℂt−1×S1 and their intersection along S1. 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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