论文标题
8D超级重力的全球异常
Global anomalies in 8d supergravity
论文作者
论文摘要
我们在八维自旋歧管上研究费米子和2型场的量规和重力异常。可能的全局量规异常是由自旋界异常组对$ω^{\ text {spin}} _ 9（bg）$进行分类的，我们通过光谱序列技术确定，我们还确定了它们的显式发电机歧管。事实证明，任何简单的谎言组的伴随表示中的费用，以及$ 8D $ $ \ $ \ natcal {n} = 1 $超级重力理论的Gravitino具有异常。我们讨论了也出现在超级重力中的2形领域如何产生异常，从而在某些类别的超级重力理论中对这些费米昂异常取消。在另一种类别的理论中，重力野生的异常不是被2型领域取消，而是通过拓扑程度的自由度取消。它限制了时空流形的拓扑结构，这在差分分析的水平上不可见。
We study gauge and gravitational anomalies of fermions and 2-form fields on eight-dimensional spin manifolds. Possible global gauge anomalies are classified by spin bordism groups $Ω^{\text{spin}}_9(BG)$ which we determine by spectral sequence techniques, and we also identify their explicit generator manifolds. It turns out that a fermion in the adjoint representation of any simple Lie group, and a gravitino in $8d$ $\mathcal{N}=1$ supergravity theory, have anomalies. We discuss how a 2-form field, which also appears in supergravity, produces anomalies which cancel against these fermion anomalies in a certain class of supergravity theories. In another class of theories, the anomaly of the gravitino is not cancelled by the 2-form field, but by topological degrees of freedom. It gives a restriction on the topology of spacetime manifolds which is not visible at the level of differential-form analysis.
