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Title: Gauging spacetime symmetries on the worldsheet and the geometric Langlands program
Authors: Tan, M.-C. 
Keywords: BRST quantization
Conformal and W symmetry
Differential and algebraic geometry
Topological field theories
Issue Date: 1-Mar-2008
Citation: Tan, M.-C. (2008-03-01). Gauging spacetime symmetries on the worldsheet and the geometric Langlands program. Journal of High Energy Physics 2008 (3) : -. ScholarBank@NUS Repository.
Abstract: We study the two-dimensional twisted (0,2) sigma-model on various smooth complex flag manifolds G/B, and explore its relevance to the geometric Langlands program. We find that an equivalence - at the level of the holomorphic chiral algebra - between a bosonic string on G/B and a B-gauged version of itself on G, will imply an isomorphism of classical -algebras and a level relation which underlie a geometric Langlands correspondence for G = SL(N,C). This furnishes an alternative physical interpretation of the geometric Langlands correspondence for G = SL(N,C), to that demonstrated earlier by Kapustin and Witten via an electric-magnetic duality of four-dimensional gauge theory. Likewise, the Hecke operators and Hecke eigensheaves will have an alternative physical interpretation in terms of the correlation functions of local operators in the holomorphic chiral algebra of a quasi-topological sigma-model without boundaries. A forthcoming paper will investigate the interpretation of a ''quantum'' geometric Langlands correspondence for G = SL(N,C) in a similar setting, albeit with fluxes of the sigma-model moduli which induce a ''quantum'' deformation of the relevant classical algebras turned on.
Source Title: Journal of High Energy Physics
ISSN: 11266708
DOI: 10.1088/1126-6708/2008/03/033
Appears in Collections:Staff Publications

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