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摘要翻译：
Braverman和Finkelberg[ARXIV:0711.2083]将几何Langlands对偶推广到仿射Kac-Moody群中的一个新尝试，使Braverman和Finkelberg[ARXIV:0711.2083]推测出某些奇异复曲面上G-丛模空间的交上同调与关联仿射G-代数的Langlands对偶的可积表示之间的数学关系，其中G是任意单连通半单群。对于a-型群，当该猜想在很大程度上得到数学验证时，我们证明了该关系在M-理论的六维紧致下具有自然的物理解释，其中五个重合膜包裹某些hyperkahler四流形；特别地，它可以被理解为弦对偶下所产生的时空BPS谱中的一种期望不变性。通过用光滑的多Taub-Nut流形代替奇异复曲面，我们发现与Witten先前通过纯场论的考虑证明的一个密切相关的结果是一致的。通过在原分析基础上增加OM五个平面，我们论证了一个涉及非单连通D型群的类似关系也应该成立。这是第一个弦论解释A-D群的几何Langlands对偶的二维扩展到复杂曲面的例子。
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英文标题：
《Five-Branes in M-Theory and a Two-Dimensional Geometric Langlands
Duality》
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作者：
Meng-Chwan Tan
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最新提交年份：
2013
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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：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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英文摘要：
A recent attempt to extend the geometric Langlands duality to affine Kac-Moody groups, has led Braverman and Finkelberg [arXiv:0711.2083] to conjecture a mathematical relation between the intersection cohomology of the moduli space of G-bundles on certain singular complex surfaces, and the integrable representations of the Langlands dual of an associated affine G-algebra, where G is any simply-connected semisimple group. For the A-type groups, where the conjecture has been mathematically verified to a large extent, we show that the relation has a natural physical interpretation in terms of six-dimensional compactifications of M-theory with coincident five-branes wrapping certain hyperkahler four-manifolds; in particular, it can be understood as an expected invariance in the resulting spacetime BPS spectrum under string dualities. By replacing the singular complex surface with a smooth multi-Taub-NUT manifold, we find agreement with a closely related result demonstrated earlier via purely field-theoretic considerations by Witten. By adding OM five-planes to the original analysis, we argue that an analogous relation involving the non-simply-connected D-type groups, ought to hold as well. This is the first example of a string-theoretic interpretation of such a two-dimensional extension to complex surfaces of the geometric Langlands duality for the A-D groups.
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PDF链接：
https://arxiv.org/pdf/0807.1107
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