3d expansions of 5d instanton partition functions

Abstract

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 $$ {\mathrm{\mathbb{C}}}_{q,{t}^{-1}}^2\times {\mathbb{S}}^1 $$, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces ℂq×S1 $$ {\mathrm{\mathbb{C}}}_q\times {\mathbb{S}}^1 $$, ℂt−1×S1 $$ {\mathrm{\mathbb{C}}}_{t^{-1}}\times {\mathbb{S}}^1 $$ and their intersection along S1 $$ {\mathbb{S}}^1 $$. These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with W q,t correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.

Keywords

• Matrix Models
• Solitons Monopoles and Instantons
• Supersymmetric Gauge Theory