Instantons and the 5D U(1) gauge theory with extra adjoint

Abstract

In this paper we compute the partition function of 5D supersymmetric U(1) gauge theory with extra adjoint matter in general $\Omega$-background. It is well known that such partition functions encode very rich topological information. We show in particular that unlike the case with no extra matter, the partition function with extra adjoint at some special values of the parameters directly reproduces the generating function for the Poincare polynomial of the moduli space of instantons. Comparing our results with those recently obtained by Iqbal et. al., who used the refined topological vertex method, we present our comments on apparent discrepancies.

9 pages

References in corpus (9)

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• The Refined Topological Vertex
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Cited by in corpus (10)

• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• On instantons as Kaluza-Klein modes of M5-branes
• Changing the preferred direction of the refined topological vertex
• Quiver Matrix Model and Topological Partition Function in Six Dimensions
• On the 5d instanton index as a Hilbert series
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• A string realisation of $\Omega$-deformed Abelian $\mathcal{N}=2^{\ast }$ theory
• Quasi-Hopf twist and elliptic Nekrasov factor
• Modular Nekrasov-Okounkov formulas
• Quiver matrix model of ADHM type and BPS state counting in diverse dimensions