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Friday, October 3rd 2014

2:00 pm:

We study various protected quantities in five dimensional gauge theories on \mathbb{R}^4\times S^1 with eight supercharges in the presence of defects. Surface defects can be described by a certain three dimensional quiver gauge theory on \mathbb{R}^2\times S^1, whose twisted chiral ring we extensively study by various methods including classical parameter spaces of supersymmetric vacua and exact partition functions. Three dimensional mirror symmetry and integrability of the dual spin chain play important roles in our analysis. For a coupled 5d/3d system we find a convenient description using monodromy defects along the two-plane which is orthogonal to the 3d defect. We compute the corresponding 5d ramified instanton partition function and show that it solves a system of difference equations of a certain elliptic integrable many-body system. We analyze various limiting cases of our construction and identify them with many previously known integrable models.

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