Establish the generalized Springer decomposition of the low-energy vacuum structure

Establish the proposed decomposition of the low-energy sectors and Coulomb branch of two-dimensional maximally supersymmetric Yang–Mills theory with simply connected gauge group G into orbifold conformal field theories and massive vacua indexed by Lusztig cuspidal data, with orbifold groups given by the corresponding relative Weyl groups W_{G,L}.

Background

The paper proposes that the low-energy dynamics of two-dimensional N=(8,8) supersymmetric Yang–Mills theory decompose into superselection sectors indexed by cuspidal data from Lusztig’s generalized Springer correspondence. Each sector is expected to consist of an orbifold conformal field theory associated with (z(l) tensor R^8)/W_{G,L}, or a massive vacuum in the zero-dimensional case.

The proposed structure is supported by threshold-bound-state counts, comparisons with string and M-theory descriptions, and supersymmetric localization. However, the decomposition is presented as conjectural rather than proved. The paper further suggests that its strongest form should be an equivalence of holomorphic factorization algebras.