论文标题
6D $ \ MATHCAL N =（1,0）$ S^1 $和F理论的含义
6d $\mathcal N=(1,0)$ anomalies on $S^1$ and F-theory implications
论文作者
论文摘要
我们表明，在圆圈上压实的6D $ \ MATHCAL n =（1,0）$的纯仪表异常是由5D有效理论中一环的场相关的Chern-Simons项捕获的。这些术语在且仅当取消异常时就消失了。为了获得此结果，至关重要的是以保持6D Lorentz不变性的方式整合大量的Kaluza-Klein模式；经常使用的zeta功能正则不够。由于这种依赖于场的Chern-simons术语在减少三维F理论的M理论时不会出现，因此每当可以使用M/F-二维时，就会自动无异常。然后在5D $ \ MATHCAL n = 1 $降低的5D $ \ MATHCAL N = 1 $之间找到了完美的匹配，而经典M理论还原与无异常理论的一环圆圈紧凑。最后，从这个潜力中，我们将量子校正读取到量规耦合函数。
We show that the pure gauge anomalies of 6d $\mathcal N=(1,0)$ theories compactified on a circle are captured by field-dependent Chern-Simons terms appearing at one-loop in the 5d effective theories. These terms vanish if and only if anomalies are canceled. In order to obtain this result, it is crucial to integrate out the massive Kaluza-Klein modes in a way that preserves 6d Lorentz invariance; the often-used zeta-function regularization is not sufficient. Since such field-dependent Chern-Simons terms do not arise in the reduction of M-theory on a threefold, six-dimensional F-theory compactifications are automatically anomaly free, whenever the M/F-duality can be used. A perfect match is then found between the 5d $\mathcal N=1$ prepotentials of the classical M-theory reduction and one-loop circle compactification of an anomaly free theory. Finally, from this potential, we read off the quantum corrections to the gauge coupling functions.
