Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-04-15
JHEP 1109:040,2011
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, 2 figures, minor corrections and references added
Scientific paper
10.1007/JHEP09(2011)040
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.
Chen Heng-Yu
Dorey Nick
Hollowood Timothy J.
Lee Sungjay
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