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Journal of High Energy Physics

, 2014:182 | Cite as

Hilbert series for moduli spaces of instantons on ℂ2/ℤ n

  • Anindya Dey
  • Amihay Hanany
  • Noppadol Mekareeya
  • Diego Rodríguez-Gómez
  • Rak-Kyeong Seong
Open Access
Article

Abstract

We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p + 4) system with the D(p + 4) branes (with or without O(p + 4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic A n−1 ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.

Keywords

Supersymmetric gauge theory Solitons Monopoles and Instantons Conformal Field Models in String Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Anindya Dey
    • 1
  • Amihay Hanany
    • 2
  • Noppadol Mekareeya
    • 3
    • 4
  • Diego Rodríguez-Gómez
    • 5
  • Rak-Kyeong Seong
    • 2
    • 6
  1. 1.Theory Group and Texas Cosmology Center, Department of PhysicsUniversity of Texas at AustinAustinU.S.A.
  2. 2.Theoretical Physics Group, The Blackett LaboratoryImperial College LondonLondonU.K.
  3. 3.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenDeutschland
  4. 4.Theory Group, Physics Department, CERNGeneva 23Switzerland
  5. 5.Department of PhysicsUniversidad de OviedoOviedoSpain
  6. 6.School of PhysicsKorea Institute for Advanced StudySeoulSouth Korea

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