We study various protected quantities in five dimensional gauge theories on $R^4\times S^1$ with eight supercharges in the presence of defects. Surface defects can be described by a certain three dimensional quiver gauge theory on $R^2\times S^1$, 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. We compute equivariant quantum K-theoretic rings of the corresponding Nakajima quiver varieties using a universal gauge invariant prescription.
