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arXiv · 1104.3021

A New 2d/4d Duality via Integrability

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

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Heng-Yu Chen, Nick Dorey, Timothy J. Hollowood, Sungjay Lee. 2011-08-04. A New 2d/4d Duality via Integrability. https://doi.org/10.1007/jhep09(2011)040

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