Journal of High Energy Physics

, 2010:106 | Cite as

Notes on wall crossing and instanton in compactified gauge theory with matter

  • Heng-Yu Chen
  • Kirill Petunin


We study the quantum effects on the Coulomb branch of \( \mathcal{N} = 2 \) SU(2) super-symmetric Yang-Mills with fundamental matters compactified on \( {\mathbb{R}^3} \times {S^1} \), and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.


Supersymmetric gauge theory Solitons Monopoles and Instantons Extended Supersymmetry Integrable Equations in Physics 


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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WisconsinMadisonU.S.A.
  2. 2.DAMTP, Centre for Mathematical SciencesUniversity of CambridgeCambridgeU.K.

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