Vacuum Structure of Maximally Supersymmetric Two-Dimensional Gauge Theories

Abstract: We study the vacuum structure of maximally supersymmetric Yang--Mills theory in two dimensions. At low energies, the theory decomposes into superselection sectors consisting of orbifold conformal field theories and massive vacua. The sectors are indexed by the cuspidal data appearing in Lusztig's generalized Springer correspondence. This suggests an enhancement of the correspondence to holomorphic factorization algebras.