Partition function (quantum field theory)

Quantum mechanics

Supersymmetry

Pure mathematics

Mathematical physics

Quiver

Gauge theory

Surface (topology)

Physics

Mathematics

Mathematical analysis

Orbifold

Geometry

Moduli space

Superpotential

Generalization

Advances in Theoretical and Mathematical Physics

We explore the non-perturbative Dyson-Schwinger equations obeyed by the partition functions of the $\Omega$-deformed $\mathcal{N}=2, d=4$ supersymmetric linear quiver gauge theories in the presence of surface defects. We demonstrate that the partition functions of different types of defects (orbifold or vortex strings) are related by analytic continuation. We introduce Darboux coordinates on a patch of the moduli space of flat $SL(N)$-connections on a sphere with special punctures, which generalize the NRS coordinates defined in the $SL(2)$ case. Finally, we compare the generating function of the Lagrangian variety of opers in these Darboux coordinates with the effective twisted superpotential of the linear quiver theory in the two-dimensional $\Omega$-background, thereby proving the NRS conjecture and its generalization to the $SL(3)$ case.

Opers, surface defects, and Yang-Yang functional