Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
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DOI：
10.1007/jhep11(2015)123
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发表时间：
2015-04
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通讯作者：
M. Zotto;C. Vafa;Dan Xie
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作者：
M. Zotto;C. Vafa;Dan Xie
研究了T2上6维（1，0）理论的紧化.我们使用这些理论通过F-理论的几何工程，并采用镜像对称技术来解决大量的（1，0）理论，包括那些与共形物质的有效4d几何。利用这一点，我们表明，对于一个给定的6d理论，我们可以得到许多不等价的4dSCFT。其中一些方面的全球对称性的6d理论，而另一些表现出SL（2，）对偶对称性继承了全球的t2。这种构造也解释了四维仿射ADE联络理论模空间的6d起源为T2上的平坦ADE联络。在由此产生的4dCFTs中，我们发现其真空几何被LG理论捕获的理论（而不是曲线或局部CY几何）。我们从（1，0）SCFT的环形紧化中得到了类穿孔的任意亏格曲线，其中类理论的曲线通过镜像对称出现。我们还表明，这些理论的小弦版本的环形紧化可以导致类理论与任意亏格黎曼曲面上没有穿刺。
We study compactification of 6 dimensional (1, 0) theories on T 2. We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4dgeometry for a large number of the (1, 0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4dSCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL (2, ℤ) duality symmetry inherited from global diffeomorphisms of the T 2. This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T 2. Among the resulting 4dCFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of classwith punctures from toroidal compactification of (1, 0) SCFTs where the curve of the classtheory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to classtheories with no punctures on arbitrary genus Riemann surface.