Defects and Quantum Seiberg-Witten Geometry

TL;DR

This paper explores how codimension two defects in five-dimensional supersymmetric gauge theories relate to integrable systems, showing that partition functions are eigenfunctions of elliptic integrable models that quantize Seiberg-Witten geometry.

Contribution

It demonstrates the connection between Nekrasov partition functions with defects and elliptic integrable systems, providing new insights into the quantum Seiberg-Witten geometry.

Findings

Partition functions are eigenfunctions of elliptic integrable systems.

Connections established between defects, gauge theories, and integrable models.

Quantization of Seiberg-Witten geometry via these integrable systems.

Abstract

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.