摘要翻译：
研究了各种光滑复标志流形G/B上的二维扭曲（0,2)Sigma-模型，并探讨了它与几何Langlands程序的关系。我们发现，在全纯手征代数的水平上，G/B上的bosonic弦与G上的B-gauged形式之间的等价，将意味着经典W-代数的同构和G=SL(N,C）的Langlands几何对应的水平关系。这为G=SL(N,C）的几何Langlands对应关系提供了另一种物理解释，与Kapustin和Witten先前通过四维规范理论的电磁对偶性所证明的解释不同。同样，在无边界的拟拓扑Sigma模型的全纯手征代数中，Hecke算子和Hecke本征束将有另一种物理解释，即局部算子的相关函数。一篇即将发表的论文将研究G=SL(N,C）在类似的情况下的“量子”几何Langlands对应的解释，尽管sigma模型模的通量引起了相关经典代数的“量子”变形。
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英文标题：
《Gauging Spacetime Symmetries on the Worldsheet and the Geometric
  Langlands Program》
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作者：
Meng-Chwan Tan
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Quantum Algebra        量子代数
分类描述：Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群，skein理论，运算代数和图解代数，量子场论
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英文摘要：
  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 W-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.
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PDF链接：
https://arxiv.org/pdf/0710.5796