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2013

On the 5d instanton index as a Hilbert series

Rodriguez-Gomez, Diego, Zafrir, Gabi

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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 note, 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.

On the 5d instanton index as a Hilbert series · Around

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J. Bhattacharya, S. Bhattacharyya, S. Minwalla, S. Raju and , “Indices for Superconformal Field Theories in 3,5 and 6 Dimensions,” JHEP 0802
Original
2008
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Similar

R. Poghossian and M. Samsonyan, “Instantons and the 5D U(1) gauge theory with extra adjoint,” J. Phys. A 42
Original
2009
Cited alongside, same era.
S. Benvenuti, A. Hanany and N. Mekareeya, “The Hilbert Series of the One Instanton Moduli Space,” JHEP 1006
Original
2010
Cited alongside, same era.
H. -C. Kim, S. Kim, E. Koh, K. Lee, S. Lee and , “On instantons as Kaluza-Klein modes of M5-branes,” JHEP 1112
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2011
Cited alongside, same era.
H. -C. Kim, S. -S. Kim and K. Lee, “5-dim Superconformal Index with Enhanced En Global Symmetry,” JHEP 1210
Original
2012
Cited alongside, same era.
A. Iqbal, C. Vafa and , “BPS Degeneracies and Superconformal Index in Diverse Dimensions,” arXiv:1210.3605 [hep-th]

Then

C. A. Keller, N. Mekareeya, J. Song and Y. Tachikawa, “The ABCDEFG of Instantons and W-algebras,” JHEP 1203
Original
2012
Later among the works it cites.
O. Bergman and D. Rodriguez-Gomez, “5d quivers and their AdS(6) duals,” JHEP 1207
Original
2012
Later among the works it cites.
O. Bergman and D. Rodriguez-Gomez, “Probing the Higgs branch of 5d fixed point theories with dual giant gravitons in AdS(6),” JHEP 1212
Original
2012
Later among the works it cites.
A. Hanany, N. Mekareeya and S. S. Razamat, “Hilbert Series for Moduli Spaces of Two Instantons,” JHEP 1301
Original
2013
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Y.Tachikawa, “Seiberg-Witten theory and instanton counting”, U. of Tokyo Master’s Thesis, http://member.ipmu.jp/yuji.tachikawa/transp/masterthesis.pdf

Cited in the paper.

http://www.math.uiuc.edu/Macaulay2/

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