Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories
Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories
复制标题
Chern-Simons 和 Wess-Zumino-Witten 理论的 Bundle Gerbes
DOI：
10.1007/s00220-005-1376-8
复制
发表时间：
2004
影响因子：
2.4
通讯作者：
Bai
中科院分区：
文献类型：
--
作者：
A. Carey;Stuart Johnson;M. Murray;D. Stevenson;Bai
对于紧致半单李群G，我们发展了与任意带联络的主G-丛和H4（BG，BG）中的一个类相关联的Chern-Simons丛2-格和乘法丛格的理论. Chern-Simons丛2-gerbe在几何上实现了微分Cheeger-Simons不变量。我们应用这些概念来改进三维Chern-Simons泛函和与群G相关的Wess-Zumino-维滕模型之间的Dijkgraaf-维滕对应。我们这样做是通过引入提升到从H4（BG，G，G）到H3（G，G）的自然映射的bundle gerbes水平。乘法丛gerbe的概念在几何上解释了非单连通李群的这种对应关系的微妙之处。Wess-Zumino-维滕模型的影响进行了讨论。
We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal G-bundle with connection and a class in H4(BG, ℤ) for a compact semi-simple Lie group G. The Chern-Simons bundle 2-gerbe realises differential geometrically the Cheeger-Simons invariant. We apply these notions to refine the Dijkgraaf-Witten correspondence between three dimensional Chern-Simons functionals and Wess-Zumino-Witten models associated to the group G. We do this by introducing a lifting to the level of bundle gerbes of the natural map from H4(BG, ℤ) to H3(G, ℤ). The notion of a multiplicative bundle gerbe accounts geometrically for the subtleties in this correspondence for non-simply connected Lie groups. The implications for Wess-Zumino-Witten models are also discussed.