The superconformal index for N=2 5d theories contains a non-perturbative part arising from 5d instantonic operators which coincides with the Nekrasov instanton partition function. In this article, for pure gauge theories, we elaborate on the relation between such instanton index and the Hilbert series of the instanton moduli space. We propose a non-trivial identification of fugacities allowing the computation of the instanton index through the Hilbert series. We show the agreement of our proposal with existing results in the literature, as well as use it to compute the exact index for a pure U(1) gauge theory.
Bibliographical noteFunding Information:
We are grateful to Noppadol Mekareeya for very useful conversations. We would also like to thank Oren Bergman for collaboration at early stages of this project as well as for very useful conversations. We would like to thank the referee for raising relevant corrections on an early version of this paper. G.Z. is supported in part by the Israel Science Foundation under grant no. 392/09 , and the US–Israel Binational Science Foundation under grant no. 2008-072 . D.R.G. is partially supported by the research grants MICINN - 09-FPA2009-07122 and the Ramon y Cajal Fellowship MEC-DGI-CSD2007-00042 .
ASJC Scopus subject areas
- Nuclear and High Energy Physics