Splitting of surface defect partition functions and integrable systems

Understand

We study Bethe/gauge correspondence at the special locus of Coulomb moduli where the integrable system exhibits the splitting of degenerate levels.

• For this investigation, we consider the four-dimensional pure $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theory, with a half-BPS surface defect constructed with the help of an orbifold or a degenerate gauge vertex.
• We show that the non-perturbative Dyson-Schwinger equations imply the Schr\"odinger-type and the Baxter-type differential equations satisfied by the respective surface defect partition functions.
• At the special locus of Coulomb moduli the surface defect partition function splits into parts.