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摘要翻译：
本文研究了复hermitian流形$x$上全纯规范丛$\mathcale$上的“B扭曲”二维$(0,2)$杂优sigma模型的微扰方面。我们证明了该模型可以用“手征微分算子”的数学理论自然地描述。特别地，sigma模型的物理反常现象可以被重新解释为对相关顶点超代数束的全局定义的一个障碍，该顶点超代数束是由自由共形场论导出的，它在$x$上局部描述了该模型。此外，人们还可以从全纯数据的角度对sigma模型单环β函数有一个新的理解。在$(2,2)$轨迹上，我们可以用Malikov等人定义的$\it{镜像}$“手性de Rham复合物”（或CDR）来描述拓扑B-模型的半扭曲变体。在\cite{GMS1}中。通过镜像对称性，我们还可以推导出关于Calabi-Yau镜像流形对上镜像CDR的sheaf上同调与原CDR的sheaf上同调的各种猜想表达式。通过对具有扭转的非k“Ahler群流形上半扭曲模型的分析，我们还可以得到与Ben-Bassat在推广复流形的镜像对称性中所建立的数学结果相一致的CDR（及其镜像）束的结论，从而表明CDR束在推广复流形的镜像对称性研究中的一个有趣的关联。
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英文标题：
《Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex,
and Twisted Generalised Mirror Symmetry》
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作者：
Meng-Chwan Tan
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最新提交年份：
2007
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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：
In this paper, we study the perturbative aspects of a "B-twisted" two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be naturally described in terms of the mathematical theory of ``Chiral Differential Operators". In particular, the physical anomalies of the sigma model can be reinterpreted as an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on $X$. In addition, one can also obtain a novel understanding of the sigma model one-loop beta function solely in terms of holomorphic data. At the $(2,2)$ locus, one can describe the resulting half-twisted variant of the topological B-model in terms of a $\it{mirror}$ "Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via mirror symmetry, one can also derive various conjectural expressions relating the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a non-K\"ahler group manifold with torsion also allows one to draw conclusions about the corresponding sheaves of CDR (and its mirror) that are consistent with mathematically established results by Ben-Bassat in \cite{ben} on the mirror symmetry of generalised complex manifolds. These conclusions therefore suggest an interesting relevance of the sheaf of CDR in the recent study of generalised mirror symmetry.
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PDF链接：
https://arxiv.org/pdf/0705.0790
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