Abstract 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 theories on $\mathbb{R}^2\times S^1$, whose twisted chiral rings we extensively study by various methods including classical parameter spaces of supersymmetric vacua and exact partition functions. Three … Read More