In this thesis, we first derive and analyze the Gukov-Witten surface defects of four-dimensional N = 4 Super Yang-Mills (SYM) theory from little string theory. The little string theory arises from type IIB string theory compactified on an ADE singularity. Defects are introduced as D-branes wrapping the 2-cycles of the singularity. In a suitable limit, these become defects of the six-dimensional superconformal N = (2, 0) field theory, which reduces to SYM after further compactification.

We then use this geometric setting to connect to the complete nilpotent orbit classification of codimension-two defects, and find relations to ADE-type Toda CFT. We highlight the differences between the defect classification in the little string theory and its (2, 0) CFT limit, and find physical insights into nilpotent orbits and their classification by Bala-Carter labels and weighted Dynkin diagrams.