Defects and Quantum Seiberg-Witten Geometry

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.

89 pages, 8 figures, references added, typos corrected

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Cited by in corpus (6)

• Duality walls and defects in 5d N=1 theories
• Hofstadter's Butterfly in Quantum Geometry
• Expanding the Bethe/Gauge Dictionary
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings