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We generalise the analysis carried out in [arXiv:0710.5796], and find thatour previous results can be extended beyond the case of SL(N,C). In particular,we show that an equivalence--at the level of the holomorphic chiralalgebra--between a bosonic string on a smooth coset manifold G/B and a B-gaugedversion of itself on G, will imply an isomorphism of classical W-algebras and alevel relation which underlie a geometric Langlands correspondence for thesimply-laced, complex ADE-groups. In addition, as opposed to line operators andbranes of an open topological sigma-model, the Hecke operators and Heckeeigensheaves, can, instead, be physically interpreted in terms of thecorrelation functions of local operators in the holomorphic chiral algebra of aclosed, quasi-topological sigma-model. Our present results thus serve as analternative physical interpretation--to that of an electric-magnetic duality offour-dimensional gauge theory demonstrated earlier by Kapustin and Witten in[arXiv:hep-th/0604151]--of the geometric Langlands correspondence for complexADE-groups. The cases with tame and mild "ramifications" are also discussed.

Gauging Spacetime Symmetries On The Worldsheet And The Geometric Langlands Program -- II