Gauging spacetime symmetries on the worldsheet and the geometric Langlands program - II

Abstract

We generalise the analysis carried out in [1], and find that our 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 chiral algebra - between a bosonic string on a smooth coset manifold G/B and a B-gauged version of itself on G, will imply an isomorphism of classical W-algebras and a level relation which underlie a geometric Langlands correspondence for the simply-laced, complex ADE-groups. In addition, as opposed to line operators and branes of an open topological sigma-model, the Hecke operators and Hecke eigensheaves, can, instead, be physically interpreted in terms of the correlation functions of local operators in the holomorphic chiral algebra of a closed, quasi-topological sigma-model. Our present results thus serve as an alternative physical interpretation - to that of an electric-magnetic duality of four-dimensional gauge theory demonstrated earlier by Kapustin and Witten in [2] - of the geometric Langlands correspondence for complex ADE-groups. The cases with tame and mild ''ramifications'' are also discussed. © 2008 SISSA.