标题： 等变上同调与规范玻色子sigma模型 显示英文标题

标题： Equivariant Cohomology and Gauged Bosonic sigma-Models

摘要： 我们重新考察了d维玻色σ模型的Wess-Zumino项规范化的难题。 我们将这一问题表述为目标空间的等变上同调语言中，并允许通过同调分析障碍。 作为检验，我们恢复了Hull和Spence的障碍，并且找到了Hull、Rocek和de Wit发现的拓扑项的一种推广。 当对称群是紧致时，我们利用拓扑工具推导出消失定理，这些定理保证了低维（d≤4）但对多种目标流形不存在障碍。 例如，任何紧致半单李群都可以规范于三维目标空间为单连通的σ模型中。 当对称群是半单但不一定紧致时，我们利用（推测的）Sullivan意义下的等变极小模型来论证这些消失定理的持续性。 为了说服力，我们手动构造了一些这样的等变极小模型，它们可能具有独立的兴趣。 我们用两个例子说明我们的结果：d=1具有辛目标空间，以及d=2目标空间为具有双不变度量的李群。 通过Noether方法的更深入研究，得到了障碍的另一种同调解释。 该方法将障碍显示为BRST上同调中鬼数为1的类。 我们评论了与一致异常的关系。 显示英文摘要

摘要： We re-examine the problem of gauging the Wess-Zumino term of a d-dimensional bosonic sigma-model. We phrase this problem in terms of the equivariant cohomology of the target space and this allows for the homological analysis of the obstruction. As a check, we recover the obstructions of Hull and Spence and also a generalization of the topological terms found by Hull, Rocek and de Wit. When the symmetry group is compact, we use topological tools to derive vanishing theorems which guarantee the absence of obstructions for low dimension (d<=4) but for a variety of target manifolds. For example, any compact semisimple Lie group can be gauged in a three-dimensional sigma-model with simply connected target space. When the symmetry group is semisimple but not necessarily compact, we argue in favor of the persistence of these vanishing theorems by making use of (conjectural) equivariant minimal models (in the sense of Sullivan). By way of persuasion, we construct by hand a few such equivariant minimal models, which may be of independent interest. We illustrate our results with two examples: d=1 with a symplectic target space, and d=2 with target space a Lie group admitting a bi-invariant metric. An alternative homological interpretation of the obstruction is obtained by a closer study of the Noether method. This method displays the obstruction as a class in BRST cohomology at ghost number 1. We comment on the relationship with consistent anomalies.