论文标题
模量空间全息图和通量真空的有限性
Moduli Space Holography and the Finiteness of Flux Vacua
论文作者
论文摘要
提出了研究和表征在弦弦压缩中出现的田间空间的全息视角。通过研究超对称弦弦压缩中的二维模量空间来开发混凝土对应关系。有人提出，每个模量空间的边界存在理论，其关键数据由希尔伯特空间，SL（2，c） - 代数和两个特殊操作员提供。该边界数据是由渐近霍奇理论的动机以及Calabi-yau歧管模量空间上的物理指标在任何无限距离边界附近渐近造型的物理度量，该指标与SL（2，r）等静脉指标的繁殖性度量指标。模量空间上批量理论的关键部分是组值物质字段的Sigma模型。讨论了如何将其与二维重力理论耦合。然后，著名的SL（2）Orbit of Hodge理论的证据给出了经典的散装边界匹配，该定理以一种更加物理的语言进行了重新制定。将这种对应关系应用于卡拉比（Calabi-Yau）四倍紧凑型中的通量景观，结果表明，在任何共同限制一个边界附近，没有无限的自动助图真空吸尘器的尾巴。这种有限的结果是对与边界数据匹配的大量解决方案的近边界扩展的约束的结果。还可以指出，超对称通量真空吸尘器和霍奇猜想的有限结果存在着惊人的联系。
A holographic perspective to study and characterize field spaces that arise in string compactifications is suggested. A concrete correspondence is developed by studying two-dimensional moduli spaces in supersymmetric string compactifications. It is proposed that there exist theories on the boundaries of each moduli space, whose crucial data are given by a Hilbert space, an Sl(2,C)-algebra, and two special operators. This boundary data is motivated by asymptotic Hodge theory and the fact that the physical metric on the moduli space of Calabi-Yau manifolds asymptotes near any infinite distance boundary to a Poincare metric with Sl(2,R) isometry. The crucial part of the bulk theory on the moduli space is a sigma model for group-valued matter fields. It is discussed how this might be coupled to a two-dimensional gravity theory. The classical bulk-boundary matching is then given by the proof of the famous Sl(2) orbit theorem of Hodge theory, which is reformulated in a more physical language. Applying this correspondence to the flux landscape in Calabi-Yau fourfold compactifications it is shown that there are no infinite tails of self-dual flux vacua near any co-dimension one boundary. This finiteness result is a consequence of the constraints on the near boundary expansion of the bulk solutions that match to the boundary data. It is also pointed out that there is a striking connection of the finiteness result for supersymmetric flux vacua and the Hodge conjecture.
