A New 2d/4d Duality via Integrability

TL;DR

This paper proves a duality connecting 2D and 4D supersymmetric gauge theories through integrability, using saddle point analysis and Bethe Ansatz equations, and extends it to quiver gauge theories.

Contribution

It provides a rigorous proof of a 2D/4D duality conjecture using saddle point analysis and Bethe Ansatz, and generalizes the duality to quiver gauge theories.

Findings

The saddle point condition matches the Bethe Ansatz equation.

On-shell superpotentials coincide in dual theories.

Dual descriptions are identified for various quiver gauge theories.

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.