Journal of High Energy Physics

, 2011:40 | Cite as

A new 2d/4d duality via integrability

  • Heng-Yu Chen
  • Nick Dorey
  • Timothy J. Hollowood
  • Sungjay Lee


We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional partition function in the Nekrasov-Shatashvili limit. At special quantized values of the Coulomb branch moduli, the saddle point condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain which coincides with the F-term equation of the dual two-dimensional theory. The on-shell values of the superpotential in the two theories are shown to coincide in corresponding vacua. We also identify two-dimensional duals for a large set of quiver gauge theories in four dimensions and generalize our proof to these cases.


Supersymmetry and Duality Brane Dynamics in Gauge Theories Supersymmetric gauge theory Integrable Field Theories 


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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Heng-Yu Chen
    • 1
  • Nick Dorey
    • 2
  • Timothy J. Hollowood
    • 3
  • Sungjay Lee
    • 2
  1. 1.Department of PhysicsUniversity of Wisconsin-MadisonMadisonU.S.A.
  2. 2.DAMTP, Centre for Mathematical SciencesUniversity of CambridgeCambridgeU.K.
  3. 3.Department of PhysicsSwansea UniversitySwanseaU.K.

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