F-理论中的幻方与半超重态
Magic square and half-hypermultiplets in F-theory
摘要：
在六维F-理论/杂合弦论中，半超多重态只有在对应于特定的四元数凯勒对称空间时才会出现，而凯勒对称空间大多与弗赖登塔尔-提茨幻方有关。受先前在具有规范群$SU(6)$、$SO(12)$或$E_7$的F理论模型中发现的有趣的奇异结构的启发，作为最后一个神奇的例子，我们研究了非分裂$I_6$型Hirzebruch表面上椭圆纤维化的F理论，其中未破缺的规范对称性假定为$Sp(3)$。我们发现以前的F-理论模型与幻方和目前的情况下，显着的定性差异。我们认为，相关的半超多重峰出现在$E_6$点，其中半超多重峰${\bf 20}$的$SU(6)$会出现在分裂模型。我们还考虑了在$D_6$点附近的非定域物质生成问题。在说明问题是什么之后，我们通过使用分裂/非分裂过渡可以被视为圆锥形过渡的最近结果来解释为什么会这样。
英文摘要：
In six-dimensional F-theory/heterotic string theory, half-hypermultiplets arise only when they correspond to particular quaternionic Kähler symmetric spaces, which are mostly associated with the Freudenthal-Tits magic square. Motivated by the intriguing singularity structure previously found in such F-theory models with a gauge group $SU(6)$,$SO(12)$ or $E_7$, we investigate, as the final magical example, an F-theory on an elliptic fibration over a Hirzebruch surface of the non-split $I_6$ type, in which the unbroken gauge symmetry is supposed to be $Sp(3)$. We find significant qualitative differences between the previous F-theory models associated with the magic square and the present case. We argue that the relevant half-hypermultiplets arise at the $E_6$ points, where half-hypermultiplets ${\bf 20}$ of $SU(6)$ would have appeared in the split model. We also consider the problem on the non-local matter generation near the $D_6$ point. After stating what the problem is, we explain why this is so by using the recent result that a split/non-split transition can be regarded as a conifold transition.
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