A New 2d/4d Duality via Integrability
Abstract
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.
Cite
@article{arxiv.1104.3021,
title = {A New 2d/4d Duality via Integrability},
author = {Heng-Yu Chen and Nick Dorey and Timothy J. Hollowood and Sungjay Lee},
journal= {arXiv preprint arXiv:1104.3021},
year = {2011}
}
Comments
19 pages, 2 figures, minor corrections and references added