Journal of High Energy Physics

, 2014:103 | Cite as

Coulomb branch and the moduli space of instantons

  • Stefano Cremonesi
  • Giulia Ferlito
  • Amihay Hanany
  • Noppadol MekareeyaEmail author
Open Access
Regular Article - Theoretical Physics


The moduli space of instantons on ℂ2 for any simple gauge group is studied using the Coulomb branch of \( \mathcal{N}=4 \) gauge theories in three dimensions. For a given simple group G, the Hilbert series of such an instanton moduli space is computed from the Coulomb branch of the quiver given by the over-extended Dynkin diagram of G. The computation includes the cases of non-simply-laced gauge groups G, complementing the ADHM constructions which are not available for exceptional gauge groups. Even though the Lagrangian description for non-simply laced Dynkin diagrams is not currently known, the prescription for computing the Coulomb branch Hilbert series of such diagrams is very simple. For instanton numbers one and two, the results are in agreement with previous works. New results and general features for the moduli spaces of three and higher instanton numbers are reported and discussed in detail.


Supersymmetric gauge theory Solitons Monopoles and Instantons Brane Dynamics in Gauge Theories Supersymmetry and Duality 


Open Access

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Stefano Cremonesi
    • 1
  • Giulia Ferlito
    • 1
  • Amihay Hanany
    • 1
  • Noppadol Mekareeya
    • 2
    Email author
  1. 1.Theoretical Physics GroupImperial College LondonLondonU.K.
  2. 2.Theory Division, Physics DepartmentCERNGeneva 23Switzerland

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