arXiv 2103.127462021-03-23hep-thmath.AG

模空间全息的体再现

Bulk Reconstruction in Moduli Space Holography

Thomas W. Grimm, Jeroen Monnee, Damian van de Heisteeg

备注：: 44 pages plus appendices, 1 figure
DOI：: 10.1007/JHEP05(2022)010

摘要：

最近有人提出，某些UV-可完成的超对称作用可以用一个具有特殊渐近边界条件的辅助非线性σ-模型的解来刻画。该模型的时空是这些有效理论的标量场空间，而目标空间是陪集空间。我们研究这个西格玛模型没有任何参考潜在的潜在的几何描述。使用全息的方法让人想起在AdS/CFT对应体重建，然后我们推导出其近边界的二维时空的解决方案。通过对一组$ Sl(2,\mathbb{R})$边界数据的分析，我们证明了在施加单一体边界匹配条件后，近边界解是唯一固定的。重建利用了Cattani、Kaplan和Schmid在证明$Sl(2)$ -轨道定理时引入的一组复杂的递归关系。我们明确地解决这些递归关系的三组简单的边界数据，并表明他们的模型的渐近期间的Calabi-丘三倍附近的锥点，大型复杂的结构点，和Tyurin退化。

英文摘要：

It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. We study this sigma-model without any reference to a potentially underlying geometric description. Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. Specifying a set of $ Sl(2,\mathbb{R})$ boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the $Sl(2)$-orbit theorem. We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi--Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration.

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