The extended Bogomolny equations with generalized Nahm pole boundary conditions, II

Source abstract

We develop a Kobayashi–Hitchin correspondence for the extended Bogomolny equations, that is, the dimensionally reduced Kapustin–Witten equations, on the product of a compact Riemann surface Σ with R y + , with generalized Nahm pole boundary conditions at y = 0 . The correspondence is between solutions of these equations satisfying these singular boundary conditions and also limiting to flat connections as y → ∞ and certain holomorphic data consisting of triplets ( E , φ , L ) , where ( E , φ ) is a stable SL ( n + 1 , C ) Higgs pair and L ⊂ E is a holomorphic line bundle. This corroborates a prediction of Gaiotto and Witten and serves as an extension of our earlier article which treats only the SL ( 2 , R ) case.