Current algebras and differential geometry
Current algebras and differential geometry
复制标题
现代代数和微分几何
DOI：
10.1088/1126-6708/2005/03/035
复制
发表时间：
2004
影响因子：
5.4
通讯作者：
T. Strobl
中科院分区：
文献类型：
--
作者：
A. Alekseev;T. Strobl
我们证明一大类二维 σ 模型的对称性和规范对称性是由一种新型的当前代数来描述的。电流在 σ 模型的目标空间上由成对的矢量场和 1 形式标记。我们计算电流-电流换向器并分析异常消除条件，该条件可以用狄拉克结构进行几何解释，这在数学文献中已有研究。广义复结构对应于将当前代数分解为无异常子代数对。我们可以用我们的方法处理的 σ 模型包括物理和拓扑示例，带或不带 Wess-Zumino 类型项。
We show that symmetries and gauge symmetries of a large class of 2-dimensional σ-models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the σ-model. We compute the current-current commutator and analyse the anomaly cancellation condition, which can be interpreted geometrically in terms of Dirac structures, previously studied in the mathematical literature. Generalized complex structures correspond to decompositions of the current algebra into pairs of anomaly free subalgebras. σ-models that we can treat with our method include both physical and topological examples, with and without Wess-Zumino type terms.