Defects and Quantum Seiberg-Witten Geometry

Understand

We study the Nekrasov partition function of the five dimensional U(N) gauge theory with maximal supersymmetry on R^4 x S^1 in the presence of codimension two defects.

• The codimension two defects can be described either as monodromy defects, or by coupling to a certain class of three dimensional quiver gauge theories on R^2 x S^1.
• We explain how these computations are connected with both classical and quantum integrable systems.
• We check, as an expansion in the instanton number, that the aforementioned partition functions are eigenfunctions of an elliptic integrable many-body system, which quantizes the Seiberg-Witten geometry of the five-dimensional gauge theory.