Codimension two defects and the Springer correspondence

Abstract

One can associate an invariant to a large class of regular codimension two defects of the six dimensional $(0,2)$ SCFT $\mathcal{X}[j]$ using the classical Springer correspondence. Such an association allows a simple description of S-duality of associated Gaiotto-Witten boundary conditions in $\mathcal{N}=4$ SYM for arbitrary gauge group and by extension, a determination of certain local aspects of class $\mathcal{S}$ constructions. I point out that the problem of \textit{classifying} the corresponding boundary conditions in $\mathcal{N}=4$ SYM is intimately tied to possible symmetry breaking patterns in the bulk theory. Using the Springer correspondence and the representation theory of Weyl groups, I construct a pair of functors between the class of boundary conditions in the theory in the phase with broken gauge symmetry and those in the phase with unbroken gauge symmetry.

11pp, To appear in proceedings of String-Math 14 (Edmonton, Alberta)

References in corpus (1)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory